What are the solutions of the equation x4 \u2013 5×2 \u2013 36 = 0? use factoring to solve.<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The given equation is:<\/p>\n\n\n\n [ To solve this equation by factoring, follow these steps:<\/p>\n\n\n\n Notice that the equation contains (x^4) and (x^2), which suggests that substituting a new variable might simplify the equation. Let:<\/p>\n\n\n\n [ This transforms the equation into:<\/p>\n\n\n\n [ Now, you have a quadratic equation in terms of (y).<\/p>\n\n\n\n We need to factor the quadratic equation (y^2 – 5y – 36 = 0). To factor, we look for two numbers that multiply to give (-36) (the constant term) and add to give (-5) (the coefficient of (y)).<\/p>\n\n\n\n The two numbers that satisfy this condition are (-9) and (4) because:<\/p>\n\n\n\n [ So, we can factor the quadratic as:<\/p>\n\n\n\n [ Now that we have the factored form, set each factor equal to zero:<\/p>\n\n\n\n [ Solving these equations gives:<\/p>\n\n\n\n [ Recall that (y = x^2), so we now substitute back:<\/p>\n\n\n\n [ Taking the square root of both sides:<\/p>\n\n\n\n [ [ This has no real solutions because the square of a real number cannot be negative. Thus, there are no real solutions from this equation.<\/p>\n\n\n\n The real solutions to the original equation are:<\/p>\n\n\n\n [ What are the solutions of the equation x4 \u2013 5×2 \u2013 36 = 0? use factoring to solve. The Correct Answer and Explanation is : The given equation is: [x^4 – 5x^2 – 36 = 0] To solve this equation by factoring, follow these steps: Step 1: Make a substitution Notice that the equation contains […]<\/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-163180","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163180","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=163180"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/163180\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=163180"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=163180"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=163180"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
x^4 – 5x^2 – 36 = 0
]<\/p>\n\n\n\nStep 1: Make a substitution<\/h3>\n\n\n\n
y = x^2
]<\/p>\n\n\n\n
y^2 – 5y – 36 = 0
]<\/p>\n\n\n\nStep 2: Factor the quadratic equation<\/h3>\n\n\n\n
-9 \\times 4 = -36 \\quad \\text{and} \\quad -9 + 4 = -5
]<\/p>\n\n\n\n
(y – 9)(y + 4) = 0
]<\/p>\n\n\n\nStep 3: Solve for (y)<\/h3>\n\n\n\n
y – 9 = 0 \\quad \\text{or} \\quad y + 4 = 0
]<\/p>\n\n\n\n
y = 9 \\quad \\text{or} \\quad y = -4
]<\/p>\n\n\n\nStep 4: Substitute back for (x)<\/h3>\n\n\n\n
\n
x^2 = 9
]<\/p>\n\n\n\n
x = \\pm 3
]<\/p>\n\n\n\n\n
x^2 = -4
]<\/p>\n\n\n\nFinal Answer<\/h3>\n\n\n\n
x = 3 \\quad \\text{or} \\quad x = -3
]<\/p>\n","protected":false},"excerpt":{"rendered":"