What two numbers multiply to \u221235 and add to \u221218?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve for two numbers that multiply to (-35) and add to (-18), we can set up a system of equations based on these conditions. Let’s denote the two numbers as (x) and (y).<\/p>\n\n\n\n The equations can be expressed as:<\/p>\n\n\n\n From the second equation, we can express (y) in terms of (x): Next, we can substitute this expression for (y) into the first equation: Expanding this gives: To make it easier to solve, we can multiply through by (-1): Now, we can apply the quadratic formula: Calculating (\\sqrt{464}): Now substituting back into the equation gives: Calculating the two potential values for (x):<\/p>\n\n\n\n Using (x \\approx -19.77), we can find (y): However, checking the integer factors of (-35), we find that (-5) and (7) are factors that meet the criteria:<\/p>\n\n\n\n Thus, the two numbers that multiply to (-35) and add to (-18) are (-5)<\/strong> and (7)<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" What two numbers multiply to \u221235 and add to \u221218? The Correct Answer and Explanation is: To solve for two numbers that multiply to (-35) and add to (-18), we can set up a system of equations based on these conditions. Let’s denote the two numbers as (x) and (y). The equations can be expressed […]<\/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-161055","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161055","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=161055"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161055\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=161055"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=161055"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=161055"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
[
y = -18 – x
]<\/p>\n\n\n\n
[
x \\cdot (-18 – x) = -35
]<\/p>\n\n\n\n
[
-x^2 – 18x = -35
]
[
-x^2 – 18x + 35 = 0
]<\/p>\n\n\n\n
[
x^2 + 18x – 35 = 0
]<\/p>\n\n\n\n
[
x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}
]
where (a = 1), (b = 18), and (c = -35). Plugging in these values:
[
x = \\frac{-18 \\pm \\sqrt{18^2 – 4 \\cdot 1 \\cdot (-35)}}{2 \\cdot 1}
]
[
x = \\frac{-18 \\pm \\sqrt{324 + 140}}{2}
]
[
x = \\frac{-18 \\pm \\sqrt{464}}{2}
]<\/p>\n\n\n\n
[
\\sqrt{464} \\approx 21.54
]<\/p>\n\n\n\n
[
x = \\frac{-18 \\pm 21.54}{2}
]<\/p>\n\n\n\n\n
[
y = -18 – (-19.77) \\approx 1.77
]<\/p>\n\n\n\n\n