[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-508188-105":59,"doc-detail-508188-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","solving-quadratics-by-square-roots-pert-math-section-96-practice-problems","Solving Quadratics by Square Roots - PERT Math Section 9.6 - Practice Problems","","Quadratic functions are reviewed through their key features, including zeros, vertex, axis of symmetry, and opening direction, with guidance on choosing an appropriate method such as factoring, square roots, completing the square, or the quadratic formula. The worksheet provides practice problems focused on solving equations by extracting square roots and factoring into products that set equal to zero. An answer key and step-by-step explanations explain handling plus/minus square roots, eliminating non-real solutions, and using geometric area relationships.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/solving-quadratics-by-square-roots-pert-math-section-96-practice-problems/508188/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/solving-quadratics-by-square-roots-pert-math-section-96-practice-problems/508188.png","ImageObject",300,407,{"name":92,"@type":93},"Aurelia","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-05",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What methods can be used to solve quadratic functions in this worksheet?","Question",{"text":113,"@type":114},"Use factoring, square roots, completing the square, or the quadratic formula based on the form of the equation shown.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How are square root equations typically handled regarding positive and negative solutions?",{"text":118,"@type":114},"Taking square roots can introduce both positive and negative options, since squaring removes signs.",{"name":120,"@type":111,"acceptedAnswer":121},"Why does the worksheet show “No real solution” for some equations?",{"text":122,"@type":114},"When the equation rearranges to a negative number inside a square root, no real number can square to a negative, so there is no real solution.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},508188,1791404910,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":39,"preview_page_count":4},1099514068365,"https://ap-avatar.wpscdn.com/avatar/10000253d8d9f28188e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1794309523707217728","Practice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nSolving Quadratics by Square Roots  \nPERT Math 􀀏 Section 9.6  \n\n| Name:   | D | ate:   | S | core:   / 12 |\n| --- | --- | --- | --- | --- |\n\nQuick Review and Helpful Hints  \nQuadratic functions can be read through their zeros, vertex, axis of symmetry, and opening direction. Choose factoring, square roots, completing the square, or the quadratic formula based on the form you see.  \n▷ Example: Solve x2 􀀀 5x + 6 = 0 .  \nWork: Factor the quadratic: x2 􀀀 5x + 6 = (x 􀀀 2)(x 􀀀 3) . Set each factor equal to zero.  \n⋆ Answer: x = 2 or x = 3  \n♦ Practice Problems  \nSolve each problem. Show enough work that another student could follow your thinking.  \n1. Solve x2 = 49 . 6. Solve 3(x 􀀀 1)2 = 27 .  \n2. Solve x2 􀀀 16 = 0 . 7. Solve x2 + 9 = 0 over the reals.  \n3. Solve (x 􀀀 3)2 = 25 .  \n8. Solve (2x)2 = 64 .  \n4. Solve 2x2 = 50 .  \n9. Solve 5x2 􀀀 20 = 0 .  \n5. Solve (x + 4)2 = 12 .  \n10. Solve (x 􀀀 7)2 = 0 .  \n♦ Word Problems  \n11. A square has area 121 square feet. Find its side length.  \n12. A dropped object has 16t2 = 144 . Find positive t.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \n1  \nScan Me  \nPractice 􀀏 Progress 􀀏 Succeed | PERT Math  \n~~ ~~  [E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](EffortlessMath.com)[a](EffortlessMath.com)[t](EffortlessMath.com)[h](EffortlessMath.com)[.](EffortlessMath.com)[c](EffortlessMath.com)[o](EffortlessMath.com)[m](EffortlessMath.com)  \nAnswer Keys  \n1. x = 􀀆7 7.  No real solution   \n2. x = 􀀆4 8. x = 􀀆4  \n3.  x = 8 , 􀀀2  9. x = 􀀆2  \n4. x = 􀀆5 10.  x = 7   \n5.  x = 􀀀4 􀀆 2 √3  11. 11 ft  \n6.  x = 4 , 􀀀2  12. 3  \nStep-by-Step Explanations  \n1. Squaring erases signs, so both 7 and 􀀀7 work — that’s why the answer always carries a 􀀆 .  \n2. Get x2 alone 􀀂rst: x2 = 16 . Then taking the square root opens up both the positive and negative options.  \n3. Since the whole (x 􀀀 3) is squared, undo it with a root: x 􀀀 3 = 􀀆5, then solve each case.  \n4. Clear the coef􀀂cient before rooting—divide by 2 to reach x2 = 25, then take both roots.  \n5. Root both sides to get x + 4 = 􀀆√12, and since 12 = 4 􀀁 3, that simpli􀀂es to 􀀆2 √3.  \n6. Divide away the 3 􀀂rst so the square stands alone, then x 􀀀 1 = 􀀆3 gives you both answers.  \n7. This rearranges to x2 = 􀀀9, but no real number squares to a negative—so there’s nothing to 􀀂nd here.  \n8. Take the root to get 2x = 􀀆8, then split off the 2—leaving x = 􀀆4 .  \n9. Move the 20 over and divide by 5 to isolate x2 = 4, then root both sides for the 􀀆 .  \n10. Zero is special: the only way a square equals zero is if the inside is zero, sox 􀀀 7 = 0 .  \n11. Area is side squared, so the side is the square root — and lengths are positive, so just 11.  \n12. Divide by 16 to free up t2 = 9 . Time can’t be negative, so keep only the positive root.  \n[E](EffortlessMath.com)[f](EffortlessMath.com)[f](EffortlessMath.com)[o](EffortlessMath.com)[r](EffortlessMath.com)[t](EffortlessMath.com)[l](EffortlessMath.com)[e](EffortlessMath.com)[s](EffortlessMath.com)[s](EffortlessMath.com)[M](Effo","cbCaibI91l1I7bnW","https://ap.wps.com/l/cbCaibI91l1I7bnW","pdf",102978,"English","# Quick Review and Helpful Hints\n## Practice Problems\n## Word Problems\n## Answer Keys\n## Step-by-Step Explanations\n## Additional PERT Math Practice","[{\"question\":\"What methods can be used to solve quadratic functions in this worksheet?\",\"answer\":\"Use factoring, square roots, completing the square, or the quadratic formula based on the form of the equation shown.\"},{\"question\":\"How are square root equations typically handled regarding positive and negative solutions?\",\"answer\":\"Taking square roots can introduce both positive and negative options, since squaring removes signs.\"},{\"question\":\"Why does the worksheet show “No real solution” for some equations?\",\"answer\":\"When the equation rearranges to a negative number inside a square root, no real number can square to a negative, so there is no real solution.\"}]","Solving Quadratics by Square Roots - PERT Math Section 9.6 - Practice Problems | PDF",1791212327]