What are the solutions to the equation (x-2)(x-4)= 8?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the equation ((x – 2)(x – 4) = 8), we will begin by expanding the left-hand side and then solving the resulting quadratic equation.<\/p>\n\n\n\n First, apply the distributive property (also known as the FOIL method for binomials) to expand ((x – 2)(x – 4)).<\/p>\n\n\n\n [ So, the equation becomes: Now, subtract 8 from both sides of the equation to set it equal to 0: Next, factor the quadratic equation (x^2 – 6x = 0). We can factor out (x) from both terms: Now, set each factor equal to 0: Finally, we can verify the solutions by substituting (x = 0) and (x = 6) into the original equation ((x – 2)(x – 4) = 8):<\/p>\n\n\n\n Thus, the solutions to the equation ((x – 2)(x – 4) = 8) are: What are the solutions to the equation (x-2)(x-4)= 8? The Correct Answer and Explanation is: To solve the equation ((x – 2)(x – 4) = 8), we will begin by expanding the left-hand side and then solving the resulting quadratic equation. Step 1: Expand the Left-Hand Side First, apply the distributive property (also known as […]<\/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-167610","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167610","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=167610"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167610\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167610"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167610"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167610"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Expand the Left-Hand Side<\/h3>\n\n\n\n
(x – 2)(x – 4) = x(x – 4) – 2(x – 4)
]
[
= x^2 – 4x – 2x + 8
]
[
= x^2 – 6x + 8
]<\/p>\n\n\n\n
[
x^2 – 6x + 8 = 8
]<\/p>\n\n\n\nStep 2: Subtract 8 from Both Sides<\/h3>\n\n\n\n
[
x^2 – 6x + 8 – 8 = 8 – 8
]
[
x^2 – 6x = 0
]<\/p>\n\n\n\nStep 3: Factor the Quadratic Expression<\/h3>\n\n\n\n
[
x(x – 6) = 0
]<\/p>\n\n\n\nStep 4: Solve for (x)<\/h3>\n\n\n\n
[
x = 0 \\quad \\text{or} \\quad x – 6 = 0
]
[
x = 0 \\quad \\text{or} \\quad x = 6
]<\/p>\n\n\n\nStep 5: Verify the Solutions<\/h3>\n\n\n\n
\n
[
(0 – 2)(0 – 4) = (-2)(-4) = 8 \\quad \\text{(True)}
]<\/li>\n\n\n\n
[
(6 – 2)(6 – 4) = (4)(2) = 8 \\quad \\text{(True)}
]<\/li>\n<\/ul>\n\n\n\nFinal Answer:<\/h3>\n\n\n\n
[
x = 0 \\quad \\text{or} \\quad x = 6
]<\/p>\n","protected":false},"excerpt":{"rendered":"