{"id":196,"date":"2022-04-13T10:18:25","date_gmt":"2022-04-13T10:18:25","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=196"},"modified":"2024-08-25T07:54:53","modified_gmt":"2024-08-25T07:54:53","slug":"j-6-complete-the-square","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/j-6-complete-the-square\/","title":{"rendered":"J.6 Complete the square"},"content":{"rendered":"\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Complete the square<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-b6cf92496532c14e30a24b89a43abeed\" style=\"color:#d73838\"><strong>Understanding Completing the Square<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Completing the square is a technique used to rewrite a quadratic equation in the form (x + h)\u00b2 = k, where h and k are constants.<\/li>\n\n\n\n<li>This form makes it easier to solve for x by taking the square root of both sides.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-19034d78f12370e233172c9dba8388e6\" style=\"color:#eff248\"><strong>Steps to Complete the Square<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Ensure the Leading Coefficient is 1:<\/strong> If the leading coefficient (a) is not 1, divide the entire equation by a to make it 1.<\/li>\n\n\n\n<li><strong>Isolate the Quadratic and Linear Terms:<\/strong> Move the constant term (c) to the other side of the equation.<\/li>\n\n\n\n<li><strong>Add the Square of Half the Linear Coefficient:<\/strong> Add (b\/2)\u00b2 to both sides of the equation. This will create a perfect square trinomial on the left side.<\/li>\n\n\n\n<li><strong>Factor the Perfect Square Trinomial:<\/strong> The left side of the equation should now be in the form (x + h)\u00b2.<\/li>\n\n\n\n<li><strong>Solve for x:<\/strong> Take the square root of both sides and solve for x.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-050cf860bf6c839fe7fd747e8e3c1b44\" style=\"color:#a7dc4d\"><strong>Example<\/strong><\/p>\n\n\n\n<p>Solve: x\u00b2 &#8211; 6x + 2 = 0<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Step 1: The leading coefficient is already 1.<\/li>\n\n\n\n<li>Step 2: Move the constant term: x\u00b2 &#8211; 6x = -2<\/li>\n\n\n\n<li>Step 3: Add the square of half the linear coefficient: x\u00b2 &#8211; 6x + 9 = -2 + 9<\/li>\n\n\n\n<li>Step 4: Factor the perfect square trinomial: (x &#8211; 3)\u00b2 = 7<\/li>\n\n\n\n<li>Step 5: Take the square root: x &#8211; 3 = \u00b1\u221a7\n<ul class=\"wp-block-list\">\n<li>x = 3 \u00b1 \u221a7<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-d8b69838324ee862c66a20bf38a0e885\" style=\"color:#f3e817\"><strong>Key Points<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Completing the square is a useful technique for solving quadratic equations, especially when factoring is not straightforward.<\/li>\n\n\n\n<li>The goal is to create a perfect square trinomial on the left side of the equation.<\/li>\n\n\n\n<li>Adding the square of half the linear coefficient is the key step in completing the square.<\/li>\n\n\n\n<li>Once the equation is in the form (x + h)\u00b2 = k, solving for x is straightforward by taking the square root.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f3bcbc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-6841d11ecb2ecb4b3eafbc9e9588473f\" style=\"color:#b00012\"><strong>Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.<\/strong><\/p>\n\n\n\n<p><em>u<\/em><sup>2<\/sup>&nbsp;\u2212 16<em>u<\/em>&nbsp;+________<\/p>\n<\/div><\/div>\n\n\n\n<p>Add (b\/2)<sup>2<\/sup> to complete the square.<\/p>\n\n\n\n<p>u<sup>2<\/sup>-16u+(b\/2)<sup>2<\/sup> <\/p>\n\n\n\n<p>=u<sup>2<\/sup> -16u+(-16\/2)<sup>2<\/sup>         Plug in&nbsp;b<em>&nbsp;=-16<\/em><\/p>\n\n\n\n<p>=u<sup>2<\/sup> -16u+(-8)<sup>2<\/sup>            Divide<\/p>\n\n\n\n<p>=u<sup>2<\/sup> -16u+64                Square<\/p>\n\n\n\n<p>This quadratic can be written as a square,(<em>u<\/em>&nbsp;\u2212 8)<sup>2<\/sup>,so it is a perfect-square quadratic. The number needed to complete the square was 64.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b4ec9c\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-6841d11ecb2ecb4b3eafbc9e9588473f\" style=\"color:#b00012\"><strong>Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.<\/strong><\/p>\n\n\n\n<p><em>k<\/em><sup>2<\/sup>&nbsp;\u2212 6<em>k<\/em>&nbsp;+________<\/p>\n<\/div><\/div>\n\n\n\n<p>Add (b\/2)<sup>2<\/sup> to complete the square.<\/p>\n\n\n\n<p>k<sup>2<\/sup>-6k+(b\/2)<sup>2<\/sup> <\/p>\n\n\n\n<p>=k<sup>2<\/sup> -6k+(-6\/2)<sup>2<\/sup>           Plug in&nbsp;b<em>&nbsp;=&nbsp;-6<\/em><\/p>\n\n\n\n<p>=k<sup>2<\/sup> -6k+(-3)<sup>2<\/sup>             Divide<\/p>\n\n\n\n<p>=k<sup>2<\/sup> -6k+9               Square<\/p>\n\n\n\n<p>This quadratic can be written as a square,(<em>k<\/em>&nbsp;\u2212 3)<sup>2<\/sup>,so it is a perfect-square quadratic. The number needed to complete the square was 9.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#a1eadf\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-6841d11ecb2ecb4b3eafbc9e9588473f\" style=\"color:#b00012\"><strong>Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.<\/strong><\/p>\n\n\n\n<p><em>f<\/em><sup>2<\/sup>&nbsp;+ 20<em>f<\/em>&nbsp;+________<\/p>\n<\/div><\/div>\n\n\n\n<p>Add (b\/2)<sup>2<\/sup> to complete the square.<\/p>\n\n\n\n<p>f<sup>2<\/sup>+20f+(b\/2)<sup>2<\/sup> <\/p>\n\n\n\n<p>=f<sup>2<\/sup> +20f+(20\/2)<sup>2<\/sup>         Plug in&nbsp;b<em>&nbsp;=&nbsp;<\/em>20<\/p>\n\n\n\n<p>=f<sup>2<\/sup> +20f+(10)<sup>2<\/sup>            Divide<\/p>\n\n\n\n<p>=f<sup>2<\/sup> +20f+100              Square<\/p>\n\n\n\n<p>This quadratic can be written as a square,(<em>f<\/em>&nbsp;+ 10)<sup>2<\/sup>,so it is a perfect-square quadratic. The number needed to complete the square was 100.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76704\/521\/201\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-53.png\" alt=\"\" class=\"wp-image-6953\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-53.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-53-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-53-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76717\/085\/506\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-71.png\" alt=\"\" class=\"wp-image-6954\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-71.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-71-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-71-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Complete the square Key Notes : Understanding Completing the Square Steps to Complete the Square Example Solve: x\u00b2 &#8211; 6x + 2 = 0 Key Points Learn with an example Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic. u2&nbsp;\u2212 16u&nbsp;+________ Add (b\/2)2 to complete the square. u2-16u+(b\/2)2 =u2 -16u+(-16\/2)2<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/j-6-complete-the-square\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.6 Complete the square&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-196","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/196","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=196"}],"version-history":[{"count":22,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/196\/revisions"}],"predecessor-version":[{"id":13678,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/196\/revisions\/13678"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}