{"id":245800,"date":"2025-07-06T13:13:34","date_gmt":"2025-07-06T13:13:34","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245800"},"modified":"2025-07-06T13:13:36","modified_gmt":"2025-07-06T13:13:36","slug":"what-two-numbers-multiply-to-negative-64-and-add-up-to-16","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/what-two-numbers-multiply-to-negative-64-and-add-up-to-16\/","title":{"rendered":"What two numbers multiply to negative 64 and add up to 16"},"content":{"rendered":"\n<p>What two numbers multiply to negative 64 and add up to 16<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve for two numbers that multiply to -64 and add up to 16, let&#8217;s denote these numbers as xxx and yyy. According to the problem:x\u00d7y=\u221264x \\times y = -64x\u00d7y=\u221264x+y=16x + y = 16x+y=16<\/p>\n\n\n\n<p>To solve this system, we can use substitution or trial and error. However, let&#8217;s first approach this by setting up a quadratic equation.<\/p>\n\n\n\n<p>If we consider the two numbers as the roots of a quadratic equation, then the sum and product of the roots can be used to form the quadratic equation. The general form of a quadratic equation is:t2\u2212(x+y)t+x\u00d7y=0t^2 &#8211; (x + y)t + x \\times y = 0t2\u2212(x+y)t+x\u00d7y=0<\/p>\n\n\n\n<p>Substituting the values for the sum and product from the problem:t2\u221216t\u221264=0t^2 &#8211; 16t &#8211; 64 = 0t2\u221216t\u221264=0<\/p>\n\n\n\n<p>Now we need to solve this quadratic equation. To do this, we use the quadratic formula:t=\u2212b\u00b1b2\u22124ac2at = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a}t=2a\u2212b\u00b1b2\u22124ac\u200b\u200b<\/p>\n\n\n\n<p>For the equation t2\u221216t\u221264=0t^2 &#8211; 16t &#8211; 64 = 0t2\u221216t\u221264=0, the coefficients are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=1a = 1a=1<\/li>\n\n\n\n<li>b=\u221216b = -16b=\u221216<\/li>\n\n\n\n<li>c=\u221264c = -64c=\u221264<\/li>\n<\/ul>\n\n\n\n<p>Substitute these values into the quadratic formula:t=\u2212(\u221216)\u00b1(\u221216)2\u22124(1)(\u221264)2(1)t = \\frac{-(-16) \\pm \\sqrt{(-16)^2 &#8211; 4(1)(-64)}}{2(1)}t=2(1)\u2212(\u221216)\u00b1(\u221216)2\u22124(1)(\u221264)\u200b\u200bt=16\u00b1256+2562t = \\frac{16 \\pm \\sqrt{256 + 256}}{2}t=216\u00b1256+256\u200b\u200bt=16\u00b15122t = \\frac{16 \\pm \\sqrt{512}}{2}t=216\u00b1512\u200b\u200bt=16\u00b122.6272t = \\frac{16 \\pm 22.627}{2}t=216\u00b122.627\u200b<\/p>\n\n\n\n<p>Now, solve for the two possible values of ttt:t1=16+22.6272=38.6272\u224819.31t_1 = \\frac{16 + 22.627}{2} = \\frac{38.627}{2} \\approx 19.31t1\u200b=216+22.627\u200b=238.627\u200b\u224819.31t2=16\u221222.6272=\u22126.6272\u2248\u22123.31t_2 = \\frac{16 &#8211; 22.627}{2} = \\frac{-6.627}{2} \\approx -3.31t2\u200b=216\u221222.627\u200b=2\u22126.627\u200b\u2248\u22123.31<\/p>\n\n\n\n<p>Thus, the two numbers are approximately 19.31 and -3.31. When multiplied, they give approximately -64, and when added together, they give approximately 16.<\/p>\n\n\n\n<p>However, exact integer values would require adjusting the approach slightly. Would you like help with that?<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-720.jpeg\" alt=\"\" class=\"wp-image-245801\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>What two numbers multiply to negative 64 and add up to 16 The Correct Answer and Explanation is: To solve for two numbers that multiply to -64 and add up to 16, let&#8217;s denote these numbers as xxx and yyy. According to the problem:x\u00d7y=\u221264x \\times y = -64x\u00d7y=\u221264x+y=16x + y = 16x+y=16 To solve this [&hellip;]<\/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-245800","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245800","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=245800"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245800\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245800"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245800"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}