What times what equals 12 but when you add those numbers together it equals 3<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n The Correct Answer is : ( 5.275 ) and ( -2.275 )<\/strong><\/mark><\/p>\n\n\n\n To solve the equation where two numbers multiply to 12 and add up to 3, we can set up the equations based on the given conditions.<\/p>\n\n\n\n Let\u2019s denote the two numbers as ( x ) and ( y ). According to the problem, we have:<\/p>\n\n\n\n We can solve these equations step by step.<\/p>\n\n\n\n From the second equation ( x + y = 3 ), we can express ( y ) in terms of ( x ):<\/p>\n\n\n\n [ Next, we can substitute this expression for ( y ) into the first equation:<\/p>\n\n\n\n [ Expanding the left side gives:<\/p>\n\n\n\n [ Rearranging this equation leads to:<\/p>\n\n\n\n [ Multiplying through by -1 to make the leading coefficient positive:<\/p>\n\n\n\n [ Now, we can apply the quadratic formula, where ( a = 1 ), ( b = -3 ), and ( c = -12 ):<\/p>\n\n\n\n [ Substituting in the values:<\/p>\n\n\n\n [ This simplifies to:<\/p>\n\n\n\n [ [ Calculating ( \\sqrt{57} \\approx 7.55 ):<\/p>\n\n\n\n Substituting back to find ( y ):<\/p>\n\n\n\n The two numbers that multiply to 12 and add up to 3 are approximately ( 5.275 ) and ( -2.275 ). This illustrates how the properties of numbers can lead to non-integer solutions, showcasing the relationships between multiplication and addition in algebra.<\/p>\n","protected":false},"excerpt":{"rendered":" What times what equals 12 but when you add those numbers together it equals 3 The Correct Answer and Explanation is : The Correct Answer is : ( 5.275 ) and ( -2.275 ) To solve the equation where two numbers multiply to 12 and add up to 3, we can set up the equations […]<\/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-148555","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148555","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=148555"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/148555\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=148555"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=148555"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=148555"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
Step 1: Express One Variable in Terms of the Other<\/h3>\n\n\n\n
y = 3 – x
]<\/p>\n\n\n\nStep 2: Substitute into the First Equation<\/h3>\n\n\n\n
x \\cdot (3 – x) = 12
]<\/p>\n\n\n\nStep 3: Expand and Rearrange the Equation<\/h3>\n\n\n\n
3x – x^2 = 12
]<\/p>\n\n\n\n
-x^2 + 3x – 12 = 0
]<\/p>\n\n\n\n
x^2 – 3x + 12 = 0
]<\/p>\n\n\n\nStep 4: Use the Quadratic Formula<\/h3>\n\n\n\n
x = \\frac{-b \\pm \\sqrt{b^2 – 4ac}}{2a}
]<\/p>\n\n\n\n
x = \\frac{3 \\pm \\sqrt{(-3)^2 – 4 \\cdot 1 \\cdot (-12)}}{2 \\cdot 1}
]<\/p>\n\n\n\n
x = \\frac{3 \\pm \\sqrt{9 + 48}}{2}
]<\/p>\n\n\n\n
x = \\frac{3 \\pm \\sqrt{57}}{2}
]<\/p>\n\n\n\nStep 5: Finding the Values of ( x ) and ( y )<\/h3>\n\n\n\n
\n
\n
Conclusion<\/h3>\n\n\n\n