{"id":156152,"date":"2024-10-17T04:42:52","date_gmt":"2024-10-17T04:42:52","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=156152"},"modified":"2024-10-17T04:42:54","modified_gmt":"2024-10-17T04:42:54","slug":"create-a-list-of-steps","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/17\/create-a-list-of-steps\/","title":{"rendered":"Create a list of steps"},"content":{"rendered":"\n<p>Create a list of steps, in order, that will solve the following equation.<br>(x &#8211; 5)^2= 25<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To solve the equation ((x &#8211; 5)^2 = 25), follow these steps:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Steps to Solve the Equation<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify the Equation:<\/strong> Start with the given equation:<br>[<br>(x &#8211; 5)^2 = 25<br>]<\/li>\n\n\n\n<li><strong>Take the Square Root of Both Sides:<\/strong> To eliminate the square, take the square root of both sides. Remember to consider both the positive and negative square roots:<br>[<br>x &#8211; 5 = \\pm 5<br>]<\/li>\n\n\n\n<li><strong>Separate into Two Equations:<\/strong> This will give you two separate equations to solve:<br>[<br>x &#8211; 5 = 5 \\quad \\text{(1)}<br>]<br>[<br>x &#8211; 5 = -5 \\quad \\text{(2)}<br>]<\/li>\n\n\n\n<li><strong>Solve the First Equation:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For equation (1):<br>[<br>x &#8211; 5 = 5<br>]<br>Add 5 to both sides:<br>[<br>x = 10<br>]<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Solve the Second Equation:<\/strong><\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>For equation (2):<br>[<br>x &#8211; 5 = -5<br>]<br>Add 5 to both sides:<br>[<br>x = 0<br>]<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>List the Solutions:<\/strong> The solutions to the equation are:<br>[<br>x = 10 \\quad \\text{and} \\quad x = 0<br>]<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>The original equation ((x &#8211; 5)^2 = 25) involves a squared term, which indicates that we can use the property of square roots to simplify our work. Taking the square root of both sides introduces two possibilities because both a positive and a negative number, when squared, yield the same result (e.g., (5^2 = 25) and ((-5)^2 = 25)).<\/p>\n\n\n\n<p>By separating the two cases after taking the square root, we ensure we capture all potential solutions for (x). The first case (x &#8211; 5 = 5) leads directly to (x = 10), while the second case (x &#8211; 5 = -5) results in (x = 0). Thus, both values represent solutions to the original equation, confirming that the process of squaring can introduce extraneous solutions, but in this case, both derived solutions are valid.<\/p>\n\n\n\n<p>In conclusion, solving quadratic equations often involves reversing operations like squaring by applying square roots, and carefully managing the implications of those operations ensures that we find all potential solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Create a list of steps, in order, that will solve the following equation.(x &#8211; 5)^2= 25 The Correct Answer and Explanation is : To solve the equation ((x &#8211; 5)^2 = 25), follow these steps: Steps to Solve the Equation Explanation The original equation ((x &#8211; 5)^2 = 25) involves a squared term, which indicates [&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-156152","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156152","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=156152"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156152\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156152"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156152"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156152"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}