(80-x)(500+20x)=55000<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n Let’s solve the equation (80\u2212x)(500+20x)=55000(80 – x)(500 + 20x) = 55000.<\/p>\n\n\n\n First, apply the distributive property to expand the left-hand side: (80\u2212x)(500+20x)=80\u22c5500+80\u22c520x\u2212x\u22c5500\u2212x\u22c520x(80 – x)(500 + 20x) = 80 \\cdot 500 + 80 \\cdot 20x – x \\cdot 500 – x \\cdot 20x<\/p>\n\n\n\n Now simplify each term: =40000+1600x\u2212500x\u221220×2= 40000 + 1600x – 500x – 20x^2<\/p>\n\n\n\n Combine like terms: =40000+1100x\u221220×2= 40000 + 1100x – 20x^2<\/p>\n\n\n\n So the equation becomes: 40000+1100x\u221220×2=5500040000 + 1100x – 20x^2 = 55000<\/p>\n\n\n\n To solve for xx, move all terms to one side of the equation: 40000+1100x\u221220×2\u221255000=040000 + 1100x – 20x^2 – 55000 = 0<\/p>\n\n\n\n Simplify: \u221215000+1100x\u221220×2=0-15000 + 1100x – 20x^2 = 0<\/p>\n\n\n\n Multiply through by -1 to make the leading coefficient positive: 15000\u22121100x+20×2=015000 – 1100x + 20x^2 = 0<\/p>\n\n\n\n Now, we have a quadratic equation: 20×2\u22121100x+15000=020x^2 – 1100x + 15000 = 0<\/p>\n\n\n\n To simplify further, divide the entire equation by 20: x2\u221255x+750=0x^2 – 55x + 750 = 0<\/p>\n\n\n\n Use the quadratic formula to solve for xx: x=\u2212(\u221255)\u00b1(\u221255)2\u22124(1)(750)2(1)x = \\frac{-(-55) \\pm \\sqrt{(-55)^2 – 4(1)(750)}}{2(1)} x=55\u00b13025\u221230002x = \\frac{55 \\pm \\sqrt{3025 – 3000}}{2} x=55\u00b1252x = \\frac{55 \\pm \\sqrt{25}}{2} x=55\u00b152x = \\frac{55 \\pm 5}{2}<\/p>\n\n\n\n So, there are two possible solutions: x=55+52=30orx=55\u221252=25x = \\frac{55 + 5}{2} = 30 \\quad \\text{or} \\quad x = \\frac{55 – 5}{2} = 25<\/p>\n\n\n\n The two possible values for xx are 3030 and 2525.<\/p>\n","protected":false},"excerpt":{"rendered":" (80-x)(500+20x)=55000 The correct answer and explanation is: Let’s solve the equation (80\u2212x)(500+20x)=55000(80 – x)(500 + 20x) = 55000. Step 1: Expand the equation First, apply the distributive property to expand the left-hand side: (80\u2212x)(500+20x)=80\u22c5500+80\u22c520x\u2212x\u22c5500\u2212x\u22c520x(80 – x)(500 + 20x) = 80 \\cdot 500 + 80 \\cdot 20x – x \\cdot 500 – x \\cdot 20x Now […]<\/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-280561","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280561","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=280561"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/280561\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=280561"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=280561"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=280561"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Expand the equation<\/h3>\n\n\n\n
Step 2: Rearrange the equation<\/h3>\n\n\n\n
Step 3: Solve the quadratic equation<\/h3>\n\n\n\n
Step 4: Conclusion<\/h3>\n\n\n\n