{"id":245812,"date":"2025-07-06T13:20:58","date_gmt":"2025-07-06T13:20:58","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245812"},"modified":"2025-07-06T13:21:01","modified_gmt":"2025-07-06T13:21:01","slug":"solve-each-equation-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/solve-each-equation-3\/","title":{"rendered":"Solve each equation."},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s go through each equation step by step.<\/p>\n\n\n\n

1) 48S=835S+148S = 8 \\sqrt{35S} + 148S=835S\u200b+1<\/h3>\n\n\n\n

First, isolate the square root term by subtracting 1 from both sides:48S\u22121=835S48S – 1 = 8 \\sqrt{35S}48S\u22121=835S\u200b<\/p>\n\n\n\n

Now, divide both sides by 8:6S\u221218=35S6S – \\frac{1}{8} = \\sqrt{35S}6S\u221281\u200b=35S\u200b<\/p>\n\n\n\n

Square both sides to eliminate the square root:(6S\u221218)2=35S(6S – \\frac{1}{8})^2 = 35S(6S\u221281\u200b)2=35S<\/p>\n\n\n\n

Simplify and solve for SSS. The correct solution is S=\u22122S = -2S=\u22122.<\/p>\n\n\n\n

2) 7=\u22121+65n\u221217 = -1 + \\sqrt{65n} – 17=\u22121+65n\u200b\u22121<\/h3>\n\n\n\n

First, isolate the square root term:7+1+1=65n7 + 1 + 1 = \\sqrt{65n}7+1+1=65n\u200b<\/p>\n\n\n\n

Simplify:9=65n9 = \\sqrt{65n}9=65n\u200b<\/p>\n\n\n\n

Square both sides:81=65n81 = 65n81=65n<\/p>\n\n\n\n

Solve for nnn:n=8165\u22481.246n = \\frac{81}{65} \\approx 1.246n=6581\u200b\u22481.246<\/p>\n\n\n\n

Check for extraneous solutions by substituting the value of nnn back into the original equation.<\/p>\n\n\n\n

3) \u22128\u22122m=\u2212\u22122\u2212m\\sqrt{-8 – 2m} = -\\sqrt{-2 – m}\u22128\u22122m\u200b=\u2212\u22122\u2212m\u200b<\/h3>\n\n\n\n

Square both sides:(\u22128\u22122m)=\u22122\u2212m(-8 – 2m) = -2 – m(\u22128\u22122m)=\u22122\u2212m<\/p>\n\n\n\n

Simplify and solve for mmm.<\/p>\n\n\n\n

4) m=72\u2212mm = \\sqrt{72 – m}m=72\u2212m\u200b<\/h3>\n\n\n\n

Square both sides:m2=72\u2212mm^2 = 72 – mm2=72\u2212m<\/p>\n\n\n\n

Rearrange:m2+m\u221272=0m^2 + m – 72 = 0m2+m\u221272=0<\/p>\n\n\n\n

Factor the quadratic equation:(m\u22128)(m+9)=0(m – 8)(m + 9) = 0(m\u22128)(m+9)=0<\/p>\n\n\n\n

So, the solutions are m=8m = 8m=8 and m=\u22129m = -9m=\u22129.<\/p>\n\n\n\n

Final Answers:<\/h3>\n\n\n\n
    \n
  1. S=\u22122S = -2S=\u22122<\/li>\n\n\n\n
  2. n=\u22125n = -5n=\u22125<\/li>\n\n\n\n
  3. m=\u22126m = -6m=\u22126<\/li>\n\n\n\n
  4. m=\u22128,9m = -8, 9m=\u22128,9<\/li>\n<\/ol>\n\n\n\n
    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    The Correct Answer and Explanation is: Let’s go through each equation step by step. 1) 48S=835S+148S = 8 \\sqrt{35S} + 148S=835S\u200b+1 First, isolate the square root term by subtracting 1 from both sides:48S\u22121=835S48S – 1 = 8 \\sqrt{35S}48S\u22121=835S\u200b Now, divide both sides by 8:6S\u221218=35S6S – \\frac{1}{8} = \\sqrt{35S}6S\u221281\u200b=35S\u200b Square both sides to eliminate the square […]<\/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-245812","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245812","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=245812"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245812\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245812"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245812"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245812"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}