{"id":240341,"date":"2025-07-03T08:38:12","date_gmt":"2025-07-03T08:38:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=240341"},"modified":"2025-07-03T08:38:14","modified_gmt":"2025-07-03T08:38:14","slug":"solve-the-equation-x4-10x2-9","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/03\/solve-the-equation-x4-10x2-9\/","title":{"rendered":"Solve the equation: x^4 – 10x^2 = -9"},"content":{"rendered":"\n

Solve the equation: x^4 – 10x^2 = -9<\/p>\n\n\n\n

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

To solve the equation x4\u221210×2=\u22129x^4 – 10x^2 = -9×4\u221210×2=\u22129, we can begin by making a substitution to simplify it.<\/p>\n\n\n\n

    \n
  1. Substitution:<\/strong>
    Let y=x2y = x^2y=x2. This way, the equation becomes: y2\u221210y=\u22129y^2 – 10y = -9y2\u221210y=\u22129 This is now a quadratic equation in terms of yyy.<\/li>\n\n\n\n
  2. Rearranging the equation:<\/strong>
    We move all terms to one side to set the equation equal to zero: y2\u221210y+9=0y^2 – 10y + 9 = 0y2\u221210y+9=0 Now, we have a standard quadratic equation.<\/li>\n\n\n\n
  3. Solving the quadratic equation:<\/strong>
    To solve the quadratic equation y2\u221210y+9=0y^2 – 10y + 9 = 0y2\u221210y+9=0, we can use the quadratic formula: y=\u2212b\u00b1b2\u22124ac2ay = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}y=2a\u2212b\u00b1b2\u22124ac\u200b\u200b For the equation y2\u221210y+9=0y^2 – 10y + 9 = 0y2\u221210y+9=0, the coefficients are a=1a = 1a=1, b=\u221210b = -10b=\u221210, and c=9c = 9c=9. Substituting these values into the quadratic formula: y=\u2212(\u221210)\u00b1(\u221210)2\u22124(1)(9)2(1)y = \\frac{-(-10) \\pm \\sqrt{(-10)^2 – 4(1)(9)}}{2(1)}y=2(1)\u2212(\u221210)\u00b1(\u221210)2\u22124(1)(9)\u200b\u200b y=10\u00b1100\u2212362y = \\frac{10 \\pm \\sqrt{100 – 36}}{2}y=210\u00b1100\u221236\u200b\u200b y=10\u00b1642y = \\frac{10 \\pm \\sqrt{64}}{2}y=210\u00b164\u200b\u200b y=10\u00b182y = \\frac{10 \\pm 8}{2}y=210\u00b18\u200b So, we have two possible solutions for yyy: y=10+82=9ory=10\u221282=1y = \\frac{10 + 8}{2} = 9 \\quad \\text{or} \\quad y = \\frac{10 – 8}{2} = 1y=210+8\u200b=9ory=210\u22128\u200b=1<\/li>\n\n\n\n
  4. Reversing the substitution:<\/strong>
    Recall that y=x2y = x^2y=x2. So, we now substitute back:\n
      \n
    • For y=9y = 9y=9, we get x2=9x^2 = 9×2=9, which gives x=\u00b13x = \\pm 3x=\u00b13.<\/li>\n\n\n\n
    • For y=1y = 1y=1, we get x2=1x^2 = 1×2=1, which gives x=\u00b11x = \\pm 1x=\u00b11.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Final solutions:<\/strong>
      The solutions to the equation are x=3,\u22123,1,\u22121x = 3, -3, 1, -1x=3,\u22123,1,\u22121.<\/li>\n<\/ol>\n\n\n\n

      Thus, the solutions to the equation x4\u221210×2=\u22129x^4 – 10x^2 = -9×4\u221210×2=\u22129 are x=3,\u22123,1,\u22121x = 3, -3, 1, -1x=3,\u22123,1,\u22121.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Solve the equation: x^4 – 10x^2 = -9 The Correct Answer and Explanation is: To solve the equation x4\u221210×2=\u22129x^4 – 10x^2 = -9×4\u221210×2=\u22129, we can begin by making a substitution to simplify it. Thus, the solutions to the equation x4\u221210×2=\u22129x^4 – 10x^2 = -9×4\u221210×2=\u22129 are x=3,\u22123,1,\u22121x = 3, -3, 1, -1x=3,\u22123,1,\u22121.<\/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-240341","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240341","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=240341"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/240341\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=240341"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=240341"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=240341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}