{"id":33089,"date":"2025-06-23T06:24:28","date_gmt":"2025-06-23T06:24:28","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=33089"},"modified":"2025-06-23T06:24:30","modified_gmt":"2025-06-23T06:24:30","slug":"solve-the-following-quadratic-equation-by-factoring","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/solve-the-following-quadratic-equation-by-factoring\/","title":{"rendered":"Solve the following quadratic equation by factoring."},"content":{"rendered":"\n<p>Solve the following quadratic equation by factoring. 1. 2x^2 &#8211; 5x &#8211; 18 = 0 2. x^2 + 6x = 16 Please help!<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>1. Solve:<\/strong><br><strong>2x\u00b2 &#8211; 5x &#8211; 18 = 0<\/strong><\/p>\n\n\n\n<p><strong>Step 1: Multiply the coefficient of x\u00b2 (which is 2) by the constant term (which is -18)<\/strong><br>2 \u00d7 (-18) = -36<\/p>\n\n\n\n<p><strong>Step 2: Find two numbers that multiply to -36 and add to -5<\/strong><br>The numbers are -9 and 4 because:<br>-9 \u00d7 4 = -36<br>-9 + 4 = -5<\/p>\n\n\n\n<p><strong>Step 3: Rewrite the middle term using these numbers<\/strong><br>2x\u00b2 &#8211; 9x + 4x &#8211; 18 = 0<\/p>\n\n\n\n<p><strong>Step 4: Group terms and factor<\/strong><br>(2x\u00b2 &#8211; 9x) + (4x &#8211; 18) = 0<br>x(2x &#8211; 9) + 2(2x &#8211; 9) = 0<\/p>\n\n\n\n<p><strong>Step 5: Factor out the common binomial<\/strong><br>(2x &#8211; 9)(x + 2) = 0<\/p>\n\n\n\n<p><strong>Step 6: Solve for x<\/strong><br>2x &#8211; 9 = 0 or x + 2 = 0<\/p>\n\n\n\n<p><strong>First solution:<\/strong><br>2x = 9<br>x = 9\/2<\/p>\n\n\n\n<p><strong>Second solution:<\/strong><br>x = -2<\/p>\n\n\n\n<p><strong>Final Answer:<\/strong><br>x = 9\/2 or x = -2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>2. Solve:<\/strong><br><strong>x\u00b2 + 6x = 16<\/strong><\/p>\n\n\n\n<p><strong>Step 1: Bring all terms to one side<\/strong><br>x\u00b2 + 6x &#8211; 16 = 0<\/p>\n\n\n\n<p><strong>Step 2: Find two numbers that multiply to -16 and add to 6<\/strong><br>The numbers are 8 and -2 because:<br>8 \u00d7 (-2) = -16<br>8 + (-2) = 6<\/p>\n\n\n\n<p><strong>Step 3: Rewrite the equation<\/strong><br>x\u00b2 + 8x &#8211; 2x &#8211; 16 = 0<\/p>\n\n\n\n<p><strong>Step 4: Group terms and factor<\/strong><br>(x\u00b2 + 8x) &#8211; (2x + 16) = 0<br>x(x + 8) &#8211; 2(x + 8) = 0<\/p>\n\n\n\n<p><strong>Step 5: Factor out the common binomial<\/strong><br>(x + 8)(x &#8211; 2) = 0<\/p>\n\n\n\n<p><strong>Step 6: Solve for x<\/strong><br>x + 8 = 0 or x &#8211; 2 = 0<\/p>\n\n\n\n<p><strong>First solution:<\/strong><br>x = -8<\/p>\n\n\n\n<p><strong>Second solution:<\/strong><br>x = 2<\/p>\n\n\n\n<p><strong>Final Answer:<\/strong><br>x = -8 or x = 2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Explanation Summary:<\/strong><\/p>\n\n\n\n<p>Factoring is a method for solving quadratic equations by expressing them as a product of two binomials set equal to zero. Once factored, the Zero Product Property tells us that if the product of two expressions is zero, then at least one of them must be zero. This leads to simple linear equations that are easy to solve for x. The key step is to find two numbers that multiply to the product of the leading coefficient and the constant term while also adding to the middle coefficient. Rearranging and grouping terms allows for factoring by grouping, revealing the solutions. This method is reliable for many quadratic equations when factoring is possible.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-492.jpeg\" alt=\"\" class=\"wp-image-33090\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-492.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-492-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-492-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Solve the following quadratic equation by factoring. 1. 2x^2 &#8211; 5x &#8211; 18 = 0 2. x^2 + 6x = 16 Please help! The Correct Answer and Explanation is: 1. Solve:2x\u00b2 &#8211; 5x &#8211; 18 = 0 Step 1: Multiply the coefficient of x\u00b2 (which is 2) by the constant term (which is -18)2 \u00d7 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-33089","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33089","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=33089"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33089\/revisions"}],"predecessor-version":[{"id":33091,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33089\/revisions\/33091"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33089"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33089"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33089"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}