{"id":32729,"date":"2024-03-05T17:32:30","date_gmt":"2024-03-05T17:32:30","guid":{"rendered":"https:\/\/moonpreneur.com\/math-corner\/?p=32729"},"modified":"2024-03-22T07:35:13","modified_gmt":"2024-03-22T07:35:13","slug":"solve-by-factorization-method","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/solve-by-factorization-method\/","title":{"rendered":"Solve (x^2 – 11x + 28 = 0) by Factorization Method"},"content":{"rendered":"\t\t
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Today, we’ll explore a cool math quadratic equation. It’s a fun math problem, (x2<\/sup> – 11x + 28 = 0)<\/strong> for which we\u2019ll find the answer to the value of \u2018x\u2019. Don’t worry if big numbers make you go, “Howw?” We’ll take it step by step, just like putting together a jigsaw puzzle.\u00a0<\/span><\/p>

Ready to crack the code with us? Let’s jump right in. And don’t worry, we’ll break it down into simple, easy-to-follow steps.<\/span><\/p>

\"Solve<\/a><\/p>

Step 1: Recognize the type of Equation<\/b><\/span><\/h4>

Our equation (x2<\/sup> – 11x + 28 = 0)<\/strong> is quadratic because it has an (x^2) term<\/strong>. <\/span><\/p>

Quadratic equations look like (ax2<\/sup> + bx + c = 0)<\/strong>, where (a), (b), and (c) are numbers<\/strong>.<\/span><\/p>

Step 2: Factor the Expression<\/b><\/span><\/h4>

We’re going to factor the expression (x2<\/sup> – 11x + 28)<\/strong>. Here’s how:<\/span><\/p>

-> Find two numbers that multiply to (28) and add up to (-11). These numbers are (-4) and (-7).<\/span><\/p>

-> Rewrite the expression as (x – 4)(x – 7)<\/strong><\/span><\/p>

Recommended Reading:<\/strong> Algebraic Expressions<\/a><\/p>

Step 3: Apply the Zero-Product Property<\/b><\/span><\/h4>

The Zero-Product Property says if we have two things multiplying to give (0), then at least one of them must be (0). So, we set each factor equal to (0) and solve for (x).<\/span><\/p>

Step 4: Solve for (x)<\/b><\/span><\/h4>

Let’s set (x – 4 = 0)<\/strong> and (x – 7 = 0)<\/strong> and solve for (x):<\/strong><\/span><\/p>

-> (x – 4 = 0) gives (x = 4).<\/span><\/p>

-> (x – 7 = 0) gives (x = 7).<\/span><\/p>

Step 5: Verify Solutions<\/b><\/span><\/h4>

We check if (x = 4) and (x = 7) work in the original equation (x2<\/sup> – 11x + 28 = 0).<\/span><\/p>

When (x = 4):<\/strong><\/p>

-> (42<\/sup> – 11(4) + 28 = 0) simplifies to (0 = 0), which is true.<\/span><\/p>

When (x = 7):<\/strong><\/p>

-> (72<\/sup> – 11(7) + 28 = 0) simplifies to (0 = 0), which is also true.<\/span><\/p>

Recommended Reading:<\/strong> Solving x^x^x =2 using Infinite Exponent Tower Trick<\/a><\/p>

Conclusion<\/b><\/span><\/h3>

By following these simple steps, we found that the solutions to (x2<\/sup> – 11x + 28 = 0) are (x = 4) and (x = 7).<\/strong> Factoring is a handy method for solving quadratic equations. Keep practicing, and you’ll master it in no time. If you have any more questions, feel free to ask.\u00a0<\/span><\/p>

We hope this article has been helpful. If you have any questions, please feel free to comment below.<\/span><\/p>

Moonpreneur understands the needs and demands this rapidly changing technological world is bringing with it for our kids. Our expert-designed<\/span> Advanced Math course<\/span><\/a> for grades 3rd, 4th, 5th, and 6th will help your child develop math skills with hands-on lessons, excite them to learn, and help them build real-life applications.\u00a0<\/span><\/p>

Register for a free<\/span> 60-minute Advanced Math Workshop <\/span><\/a>today!<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

Today, we’ll explore a cool math quadratic equation. It’s a fun math problem, (x2 – 11x + 28 = 0) for which we\u2019ll find the answer to the value of \u2018x\u2019. Don’t worry if big numbers make you go, “Howw?” We’ll take it step by step, just like putting together a jigsaw puzzle.\u00a0 Ready to […]<\/p>\n","protected":false},"author":116,"featured_media":32735,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[979],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/32729"}],"collection":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/comments?post=32729"}],"version-history":[{"count":22,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/32729\/revisions"}],"predecessor-version":[{"id":32893,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/32729\/revisions\/32893"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media\/32735"}],"wp:attachment":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media?parent=32729"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/categories?post=32729"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/tags?post=32729"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}