{"id":33084,"date":"2025-06-23T06:22:04","date_gmt":"2025-06-23T06:22:04","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=33084"},"modified":"2025-06-23T06:22:06","modified_gmt":"2025-06-23T06:22:06","slug":"use-factoring-to-solve-the-equation","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/use-factoring-to-solve-the-equation\/","title":{"rendered":"Use factoring to solve the equation."},"content":{"rendered":"\n<p>Use factoring to solve the equation. 15) 3x^2 &#8211; 5x &#8211; 18 = 0 A) -2, -3 B) 2, 3 C) 3, 2, 3 D) 0, 2, 3 Solve by the square-root property: 16) (x + 4)^2 = 20 A) 2 &#8211; \u00e2\u02c6\u016115, -5 B) 4 &#8211; 2\u00e2\u02c6\u016115, 4 + 2\u00e2\u02c6\u016115 C) 2 &#8211; \u00e2\u02c6\u016145, 2 + \u00e2\u02c6\u016145 D) 4 + 2\u00e2\u02c6\u016116, -4 &#8211; 2\u00e2\u02c6\u016116<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"340\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-236.png\" alt=\"\" class=\"wp-image-33085\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-236.png 1024w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-236-300x100.png 300w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/image-236-768x255.png 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\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>Let\u2019s tackle both problems step by step using the appropriate algebraic methods.<\/p>\n\n\n\n<p><strong>Problem 15: Factor the quadratic equation<\/strong> Given: 3&#215;2\u22125x\u221218=03x^2 &#8211; 5x &#8211; 18 = 0<\/p>\n\n\n\n<p>We begin by looking for two numbers whose product is 3\u00d7\u221218=\u2212543 \\times -18 = -54 and whose sum is \u22125-5. These numbers are \u22129-9 and 66.<\/p>\n\n\n\n<p>Rewrite the middle term: 3&#215;2\u22129x+6x\u221218=03x^2 &#8211; 9x + 6x &#8211; 18 = 0<\/p>\n\n\n\n<p>Group terms: (3&#215;2\u22129x)+(6x\u221218)=0(3x^2 &#8211; 9x) + (6x &#8211; 18) = 0<\/p>\n\n\n\n<p>Factor each group: 3x(x\u22123)+6(x\u22123)=03x(x &#8211; 3) + 6(x &#8211; 3) = 0<\/p>\n\n\n\n<p>Now factor the common binomial: (3x+6)(x\u22123)=0(3x + 6)(x &#8211; 3) = 0<\/p>\n\n\n\n<p>Divide out the constant: 3(x+2)(x\u22123)=03(x + 2)(x &#8211; 3) = 0<\/p>\n\n\n\n<p>Set each factor equal to zero: x+2=0x + 2 = 0 gives x=\u22122x = -2 x\u22123=0x &#8211; 3 = 0 gives x=3x = 3<\/p>\n\n\n\n<p><strong>Answer: A) -2, -3<\/strong><\/p>\n\n\n\n<p><strong>Problem 16: Solve using the square-root property<\/strong> Given: (x+4)2=20(x + 4)^2 = 20<\/p>\n\n\n\n<p>Apply the square-root property: x+4=\u00b120x + 4 = \\pm \\sqrt{20}<\/p>\n\n\n\n<p>Simplify the radical: 20=4\u22c55=25\\sqrt{20} = \\sqrt{4 \\cdot 5} = 2\\sqrt{5} So: x+4=\u00b125x + 4 = \\pm 2\\sqrt{5}<\/p>\n\n\n\n<p>Now isolate x: x=\u22124\u00b125x = -4 \\pm 2\\sqrt{5}<\/p>\n\n\n\n<p>Thus, the two solutions are: x=\u22124+25x = -4 + 2\\sqrt{5} and x=\u22124\u221225x = -4 &#8211; 2\\sqrt{5}<\/p>\n\n\n\n<p><strong>Answer: B) -4 + 2\u221a5, -4 &#8211; 2\u221a5<\/strong><\/p>\n\n\n\n<p>Both problems demonstrate classic quadratic solution methods. Factoring rewrites the equation into a product of binomials to extract roots directly, while the square-root property isolates a squared term and solves through root manipulation. These skills are essential for mastering algebraic analysis.<\/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-banner8-491.jpeg\" alt=\"\" class=\"wp-image-33086\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-491.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-491-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-491-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Use factoring to solve the equation. 15) 3x^2 &#8211; 5x &#8211; 18 = 0 A) -2, -3 B) 2, 3 C) 3, 2, 3 D) 0, 2, 3 Solve by the square-root property: 16) (x + 4)^2 = 20 A) 2 &#8211; \u00e2\u02c6\u016115, -5 B) 4 &#8211; 2\u00e2\u02c6\u016115, 4 + 2\u00e2\u02c6\u016115 C) 2 &#8211; \u00e2\u02c6\u016145, [&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-33084","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33084","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=33084"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33084\/revisions"}],"predecessor-version":[{"id":33087,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/33084\/revisions\/33087"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=33084"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=33084"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=33084"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}