What constant should be added to the binomial x2 + 5x so that it becomes a perfect square trinomial?<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To make the binomial ( x^2 + 5x ) into a perfect square trinomial, we need to add a constant that will complete the square.<\/p>\n\n\n\n A perfect square trinomial takes the form: So, the constant that we need to add to ( x^2 + 5x ) is ( 6.25 ).<\/p>\n\n\n\n By adding 6.25 to ( x^2 + 5x ), we get: Now, this expression can be written as a perfect square trinomial: Completing the square is a common method used in algebra to transform a quadratic expression into a perfect square trinomial. This approach is useful for solving quadratic equations, graphing parabolas, and integrating certain functions in calculus.<\/p>\n\n\n\n In our example, the binomial ( x^2 + 5x ) was missing a constant to make it a perfect square. The process involved finding half of the ( x )-term coefficient (5), squaring it, and then adding this square (6.25) to the binomial. The resulting trinomial, ( x^2 + 5x + 6.25 ), can then be factored as ( (x + 2.5)^2 ), which is the square of a binomial.<\/p>\n\n\n\n By adding 6.25, we completed the square, transforming the expression into an easier-to-manage form, useful for further algebraic manipulations or solving equations.<\/p>\n","protected":false},"excerpt":{"rendered":" What constant should be added to the binomial x2 + 5x so that it becomes a perfect square trinomial? The Correct Answer and Explanation is: To make the binomial ( x^2 + 5x ) into a perfect square trinomial, we need to add a constant that will complete the square. Solution: A perfect square trinomial […]<\/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-159479","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159479","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=159479"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159479\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=159479"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=159479"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=159479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Solution:<\/h3>\n\n\n\n
[
(a + b)^2 = a^2 + 2ab + b^2
]
In our case, ( x^2 + 5x ) is missing the last term, which is necessary to create a perfect square. To find the constant that will complete the square, we can follow these steps:<\/p>\n\n\n\n\n
[
\\frac{5}{2} = 2.5
]<\/li>\n\n\n\n
[
(2.5)^2 = 6.25
]<\/li>\n<\/ol>\n\n\n\nFinal Expression:<\/h3>\n\n\n\n
[
x^2 + 5x + 6.25
]<\/p>\n\n\n\n
[
(x + 2.5)^2
]<\/p>\n\n\n\nExplanation:<\/h3>\n\n\n\n