{"id":276658,"date":"2025-07-31T07:28:40","date_gmt":"2025-07-31T07:28:40","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=276658"},"modified":"2025-07-31T07:28:43","modified_gmt":"2025-07-31T07:28:43","slug":"complete-the-square","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/31\/complete-the-square\/","title":{"rendered":"Complete the square.\u00a0"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/image-1325.png\" alt=\"\" class=\"wp-image-276659\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>81<\/strong><\/p>\n\n\n\n<p>The problem asks you to complete the square for the quadratic expression&nbsp;j\u00b2 + 18j. Completing the square is a technique used to transform a quadratic expression of the form&nbsp;ax\u00b2 + bx + c&nbsp;into a perfect square trinomial, which is a trinomial that can be factored as&nbsp;(x + k)\u00b2&nbsp;or&nbsp;(x &#8211; k)\u00b2.<\/p>\n\n\n\n<p>A perfect square trinomial follows the pattern&nbsp;(x + k)\u00b2 = x\u00b2 + 2kx + k\u00b2. Our goal is to find the constant term,&nbsp;k\u00b2, that will make the given expression&nbsp;j\u00b2 + 18j&nbsp;fit this pattern.<\/p>\n\n\n\n<p>In our expression,&nbsp;j&nbsp;takes the place of&nbsp;x. We can compare&nbsp;j\u00b2 + 18j&nbsp;to the first two terms of the perfect square formula,&nbsp;j\u00b2 + 2kj.<\/p>\n\n\n\n<p>By comparing the middle terms,&nbsp;18j&nbsp;and&nbsp;2kj, we can see that&nbsp;2k&nbsp;must be equal to 18.<br>To find the value of&nbsp;k, we solve this simple equation:<br>2k = 18<br>k = 18 \/ 2<br>k = 9<\/p>\n\n\n\n<p>The number we need to add to complete the square is&nbsp;k\u00b2. Since we have found that&nbsp;k = 9, we just need to square this value:<br>k\u00b2 = 9\u00b2 = 81<\/p>\n\n\n\n<p>Therefore, the number that completes the square is 81.<\/p>\n\n\n\n<p>When we add 81 to the original expression, we get&nbsp;j\u00b2 + 18j + 81. This is a perfect square trinomial because it can be factored into&nbsp;(j + 9)\u00b2. We can verify this by expanding&nbsp;(j + 9)\u00b2, which gives us&nbsp;(j + 9)(j + 9) = j\u00b2 + 9j + 9j + 81 = j\u00b2 + 18j + 81, confirming our result. The procedure provides a reliable method for finding the missing term in any such quadratic expression.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2644.jpeg\" alt=\"\" class=\"wp-image-276665\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The Correct Answer and Explanation is: 81 The problem asks you to complete the square for the quadratic expression&nbsp;j\u00b2 + 18j. Completing the square is a technique used to transform a quadratic expression of the form&nbsp;ax\u00b2 + bx + c&nbsp;into a perfect square trinomial, which is a trinomial that can be factored as&nbsp;(x + k)\u00b2&nbsp;or&nbsp;(x [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-276658","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/276658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=276658"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/276658\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=276658"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=276658"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=276658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}