Solve (x-3)^2=5<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To solve the equation ((x – 3)^2 = 5), follow these steps:<\/p>\n\n\n\n Since ((x – 3)^2 = 5), we can take the square root of both sides to undo the square on the left-hand side. However, remember that when you take the square root of a number, you need to account for both the positive and negative roots.<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ To solve for (x), we now need to add 3 to both sides of the equation to isolate (x). This gives:<\/p>\n\n\n\n [ The (\\pm) symbol means there are two possible solutions: one where you add (\\sqrt{5}) to 3, and one where you subtract (\\sqrt{5}) from 3. Thus, the two solutions are:<\/p>\n\n\n\n [ We can approximate (\\sqrt{5}). Since (\\sqrt{5} \\approx 2.236), we can substitute this value to get approximate numerical solutions.<\/p>\n\n\n\n [ [ Thus, the approximate solutions to the equation ((x – 3)^2 = 5) are:<\/p>\n\n\n\n [ This problem involves solving a quadratic equation. The first step is to recognize that the square of a binomial, ((x – 3)^2), means that (x – 3) is being multiplied by itself. To isolate (x), you must undo this operation by taking the square root of both sides, and then apply the principle that squaring a number results in both a positive and negative root. Finally, by simplifying and approximating the square root of 5, you obtain the two possible solutions for (x).<\/p>\n","protected":false},"excerpt":{"rendered":" Solve (x-3)^2=5 The Correct Answer and Explanation is : To solve the equation ((x – 3)^2 = 5), follow these steps: Step 1: Remove the square by taking the square root of both sides. Since ((x – 3)^2 = 5), we can take the square root of both sides to undo the square on the […]<\/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-170300","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170300","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=170300"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/170300\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=170300"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=170300"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=170300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Remove the square by taking the square root of both sides.<\/h3>\n\n\n\n
\\sqrt{(x – 3)^2} = \\pm \\sqrt{5}
]<\/p>\n\n\n\n
x – 3 = \\pm \\sqrt{5}
]<\/p>\n\n\n\nStep 2: Isolate (x).<\/h3>\n\n\n\n
x = 3 \\pm \\sqrt{5}
]<\/p>\n\n\n\nStep 3: Express the two possible solutions.<\/h3>\n\n\n\n
x = 3 + \\sqrt{5} \\quad \\text{or} \\quad x = 3 – \\sqrt{5}
]<\/p>\n\n\n\nStep 4: Approximate the solutions.<\/h3>\n\n\n\n
\n
x \\approx 3 + 2.236 = 5.236
]<\/p>\n\n\n\n\n
x \\approx 3 – 2.236 = 0.764
]<\/p>\n\n\n\n
x \\approx 5.236 \\quad \\text{or} \\quad x \\approx 0.764
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n