{"id":157511,"date":"2024-10-22T07:05:11","date_gmt":"2024-10-22T07:05:11","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=157511"},"modified":"2024-10-22T07:05:14","modified_gmt":"2024-10-22T07:05:14","slug":"what-is-the-solutions-to-x2-equals-8","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/22\/what-is-the-solutions-to-x2-equals-8\/","title":{"rendered":"What is the solutions to X2 equals 8\u200b"},"content":{"rendered":"\n

What is the solutions to X2 equals 8\u200b<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To solve the equation ( x^2 = 8 ), we need to isolate ( x ). The equation is a simple quadratic equation where ( x ) is squared. Here are the steps to find the solutions:<\/p>\n\n\n\n

    \n
  1. Isolate ( x^2 )<\/strong>: The equation is already in a suitable form, with ( x^2 ) on one side and ( 8 ) on the other.<\/li>\n\n\n\n
  2. Take the square root of both sides<\/strong>: To solve for ( x ), we take the square root of both sides of the equation. However, it’s important to remember that taking the square root can yield both a positive and a negative solution. Thus, we write:
    [
    x = \\pm \\sqrt{8}
    ]<\/li>\n\n\n\n
  3. Simplify ( \\sqrt{8} )<\/strong>: The square root of ( 8 ) can be simplified further. We know that:
    [
    \\sqrt{8} = \\sqrt{4 \\times 2} = \\sqrt{4} \\times \\sqrt{2} = 2\\sqrt{2}
    ]
    Therefore, we can rewrite our solutions as:
    [
    x = \\pm 2\\sqrt{2}
    ]<\/li>\n\n\n\n
  4. Final solutions<\/strong>: This means that the solutions to the equation ( x^2 = 8 ) are:
    [
    x = 2\\sqrt{2} \\quad \\text{and} \\quad x = -2\\sqrt{2}
    ]<\/li>\n<\/ol>\n\n\n\n

    Explanation:<\/h3>\n\n\n\n

    Quadratic equations, like ( x^2 = c ) (where ( c ) is a positive number), will always yield two solutions due to the nature of squaring a number. When ( x ) is squared, both ( x ) and ( -x ) will produce the same positive value, ( c ). In this case, squaring ( 2\\sqrt{2} ) or ( -2\\sqrt{2} ) gives ( 8 ), confirming that both values are valid solutions.<\/p>\n\n\n\n

    Quadratic equations can be graphed as parabolas, which are U-shaped curves. The equation ( y = x^2 ) would intersect the horizontal line ( y = 8 ) at two points: ( x = 2\\sqrt{2} ) and ( x = -2\\sqrt{2} ). This graphical representation reinforces the idea that there are two solutions.<\/p>\n\n\n\n

    Thus, the complete solution set for the equation ( x^2 = 8 ) is:
    [
    x = 2\\sqrt{2} \\quad \\text{and} \\quad x = -2\\sqrt{2}
    ]<\/p>\n","protected":false},"excerpt":{"rendered":"

    What is the solutions to X2 equals 8\u200b The Correct Answer and Explanation is: To solve the equation ( x^2 = 8 ), we need to isolate ( x ). The equation is a simple quadratic equation where ( x ) is squared. Here are the steps to find the solutions: Explanation: Quadratic equations, like […]<\/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-157511","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157511","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=157511"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157511\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=157511"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=157511"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=157511"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}