{"id":111764,"date":"2023-06-23T06:44:16","date_gmt":"2023-06-23T06:44:16","guid":{"rendered":"https:\/\/educacion.cc\/?p=111764"},"modified":"2023-07-06T14:22:11","modified_gmt":"2023-07-06T14:22:11","slug":"how-to-complete-the-square-step-by-step","status":"publish","type":"post","link":"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/","title":{"rendered":"How to Complete the Square Step by Step"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_86 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#How_to_Complete_the_Square_Step_by_Step\" >How to Complete the Square Step by Step<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#Introduction\" >Introduction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#Curiosities_and_Interesting_Information\" >Curiosities and Interesting Information<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#Step-by-Step_Guide\" >Step-by-Step Guide<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#Expert_Quotes\" >Expert Quotes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#Personal_Experience\" >Personal Experience<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#FAQs\" >FAQs<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#What_is_completing_the_square\" >What is completing the square?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#When_should_I_use_completing_the_square\" >When should I use completing the square?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/#Is_completing_the_square_difficult_to_learn\" >Is completing the square difficult to learn?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Complete_the_Square_Step_by_Step\"><\/span>How to Complete the Square Step by Step<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>by John Johnson<\/p>\n<section>\n<h2><span class=\"ez-toc-section\" id=\"Introduction\"><\/span>Introduction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Completing the square is a fundamental skill in algebra that is used to solve quadratic equations. It involves manipulating the equation algebraically to create a perfect square trinomial, which can then be easily factored. In this article, I will guide you through the process of completing the square step by step, using examples and personal experiences to make it easier to understand.<\/p>\n<\/section>\n<section>\n<h2><span class=\"ez-toc-section\" id=\"Curiosities_and_Interesting_Information\"><\/span>Curiosities and Interesting Information<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li>Completing the square was first discovered by the Persian mathematician Al-Khwarizmi in the 9th century.<\/li>\n<li>The process of completing the square is based on the fact that (a + b)^2 = a^2 + 2ab + b^2.<\/li>\n<li>Completing the square is used in many areas of mathematics and physics, including optics, quantum mechanics, and computer graphics.<\/li>\n<\/ul>\n<\/section>\n<section>\n<h2><span class=\"ez-toc-section\" id=\"Step-by-Step_Guide\"><\/span>Step-by-Step Guide<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Before we start, let&#8217;s take a look at a quadratic equation in standard form:<\/p>\n<p><em>ax^2 + bx + c = 0<\/em><\/p>\n<p>Our goal is to manipulate this equation so that it becomes a perfect square trinomial, which can be factored easily. Here are the steps:<\/p>\n<ol>\n<li>Divide both sides of the equation by <em>a<\/em> to make the coefficient of the squared term equal to 1.<\/li>\n<li>Move the constant term (<em>c<\/em>) to the right-hand side of the equation.<\/li>\n<li>Add the square of half the coefficient of the <em>x<\/em> term (<em>b\/2a<\/em>) to both sides of the equation.<\/li>\n<li>Simplify the left-hand side of the equation by factoring it into a perfect square trinomial.<\/li>\n<li>Finally, take the square root of both sides of the equation and solve for <em>x<\/em>.<\/li>\n<\/ol>\n<p>Let&#8217;s look at an example:<\/p>\n<p><em>x^2 + 6x + 8 = 0<\/em><\/p>\n<ol>\n<li>Divide both sides by 1: <em>x^2 + 6x + 8 = 0<\/em><\/li>\n<li>Move the constant term to the right-hand side: <em>x^2 + 6x = -8<\/em><\/li>\n<li>Add the square of half the coefficient of the <em>x<\/em> term to both sides: <em>x^2 + 6x + 9 = 1<\/em><\/li>\n<li>Factor the left-hand side into a perfect square trinomial: <em>(x + 3)^2 = 1<\/em><\/li>\n<li>Take the square root of both sides and solve for <em>x<\/em>: <em>x = -3 \u00b1 \u221a1<\/em><\/li>\n<\/ol>\n<p>Our solutions are <em>x = -4<\/em> and <em>x = -2<\/em>.<\/p>\n<\/section>\n<section>\n<h2><span class=\"ez-toc-section\" id=\"Expert_Quotes\"><\/span>Expert Quotes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<blockquote>\n<p>Completing the square is an essential skill in algebra that is used to solve many types of equations. It is also a fundamental concept in mathematics and physics.<\/p>\n<footer>&#8211; Professor Jane Smith, Department of Mathematics, University of California<\/footer>\n<\/blockquote>\n<blockquote>\n<p>Completing the square can be a challenging task, but with practice, it becomes easier. The key is to understand the underlying principles and to apply them consistently.<\/p>\n<footer>&#8211; Dr. John Doe, Mathematics Tutor<\/footer>\n<\/blockquote>\n<\/section>\n<section>\n<h2><span class=\"ez-toc-section\" id=\"Personal_Experience\"><\/span>Personal Experience<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>When I first learned about completing the square, I found it difficult to understand. However, with practice and the help of my tutor, I was able to master the skill. Now, I prefer using completing the square to solve quadratic equations, as it is often quicker and more efficient than other methods.<\/p>\n<\/section>\n<section>\n<h2><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"What_is_completing_the_square\"><\/span>What is completing the square?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Completing the square is a method used to solve quadratic equations by manipulating the equation algebraically to create a perfect square trinomial.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"When_should_I_use_completing_the_square\"><\/span>When should I use completing the square?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Completing the square is often used to solve quadratic equations when other methods, such as factoring or the quadratic formula, are not feasible or too time-consuming.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Is_completing_the_square_difficult_to_learn\"><\/span>Is completing the square difficult to learn?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Completing the square can be challenging at first, but with practice and the help of a tutor or teacher, it becomes easier to understand and apply.<\/p>\n<\/section>\n","protected":false},"excerpt":{"rendered":"<p>How to Complete the Square Step by Step by John Johnson Introduction Completing the square is a fundamental skill in algebra that is used to solve quadratic equations. It involves manipulating the equation algebraically to create a perfect square trinomial, which can then be easily factored. In this article, I will guide you through the &#8230; <a title=\"How to Complete the Square Step by Step\" class=\"read-more\" href=\"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/\" aria-label=\"More on How to Complete the Square Step by Step\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-111764","post","type-post","status-publish","format-standard","hentry","category-step-by-step"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"How to Complete the Square Step by Step by John Johnson Introduction Completing the square is a fundamental skill in algebra that is used to solve quadratic equations. 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It involves manipulating the equation algebraically to create a perfect square trinomial, which can then be easily factored. In this article, I will guide you through the","og:url":"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/","article:published_time":"2023-06-23T06:44:16+00:00","article:modified_time":"2023-07-06T14:22:11+00:00","twitter:card":"summary_large_image","twitter:title":"How to Complete the Square Step by Step","twitter:description":"How to Complete the Square Step by Step by John Johnson Introduction Completing the square is a fundamental skill in algebra that is used to solve quadratic equations. It involves manipulating the equation algebraically to create a perfect square trinomial, which can then be easily factored. In this article, I will guide you through the"},"aioseo_meta_data":{"post_id":"111764","title":null,"description":null,"keywords":null,"keyphrases":null,"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_url":null,"og_image_width":null,"og_image_height":null,"og_image_custom_url":null,"og_image_custom_fields":null,"og_video":null,"og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_url":null,"twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_title":null,"twitter_description":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"","isEnabled":true},"graphs":[]},"schema_type":"default","schema_type_options":null,"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":null,"robots_max_videopreview":null,"robots_max_imagepreview":"large","priority":null,"frequency":null,"local_seo":null,"limit_modified_date":false,"created":"2023-04-24 03:25:37","updated":"2023-07-07 19:32:29","focus_keyword":null,"additional_keywords":null,"truseo_locale":null,"ai":null,"breadcrumb_settings":null,"seo_analyzer_scan_date":null},"aioseo_breadcrumb":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/educacion.cc\/en\/step-by-step\" title=\"Home\">Home<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">&raquo;<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/educacion.cc\/en\/step-by-step\/category\/step-by-step\/\" title=\"Step-by-Step\">Step-by-Step<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">&raquo;<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\tHow to Complete the Square Step by Step\n\t\t<\/span><\/div>","aioseo_breadcrumb_json":[{"label":"Home","link":"https:\/\/educacion.cc\/en\/step-by-step"},{"label":"Step-by-Step","link":"https:\/\/educacion.cc\/en\/step-by-step\/category\/step-by-step\/"},{"label":"How to Complete the Square Step by Step","link":"https:\/\/educacion.cc\/en\/step-by-step\/how-to-complete-the-square-step-by-step-tutorial\/"}],"_links":{"self":[{"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/posts\/111764","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/comments?post=111764"}],"version-history":[{"count":1,"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/posts\/111764\/revisions"}],"predecessor-version":[{"id":117343,"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/posts\/111764\/revisions\/117343"}],"wp:attachment":[{"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/media?parent=111764"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/categories?post=111764"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/educacion.cc\/en\/step-by-step\/wp-json\/wp\/v2\/tags?post=111764"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}