Chapter 8: Q25. (page 492)

Solve each equation. Check your solutions.
$24 + x^{2} = 10 x$

Short Answer

Expert verified

The solution of $24 + x^{2} = 10$ is $x = 4, 6$ .

Step by step solution

Step 1. Subtract.

Subtract $10 x$ from both the sides of the given equation.

role="math" localid="1647952589882" $24 + x^{2} - 10 x = 10 x - 10 x = 0$

Step 2. Factor by using GCF.

Factor by using GCF to get the form $x y = 0$ .

$(x - 4) (x - 6) = 0$

Step 3. Write zero product property.

For any real numbers $x$ and $y$ , if $x y = 0$ then $x = 0, y = 0$ or both $x$ and $y$ equal to zero.

Step 4. Apply zero product property.

Apply zero product property to the given equation, $(x - 4) (x - 6) = 0$ .

$x - 4 = 0 or x - 6 = 0 x = 4 x = 6$

Therefore, the roots are 4 and 6.

Step 5. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute 4 for $x$ and 6 for $x$ in the given equation and simplify.

role="math" localid="1647952986538" $24 + {(4)}^{2} \overset{?}{=} 10 (4) 40 = 40 L H S = R H S$

role="math" localid="1647952992003" $24 + {(6)}^{2} \overset{?}{=} 10 (6) 60 = 60 L H S = R H S$

Therefore, the obtained solution is correct.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve each equation. Check your solutions.
$24 + x^{2} = 10 x$

Short Answer

Step by step solution

Step 1. Subtract.

Step 2. Factor by using GCF.

Step 3. Write zero product property.

Step 4. Apply zero product property.

Step 5. Check the obtained solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Probability and Statistics

Mechanics Maths

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solutions.24+x2=10x

Short Answer

Step by step solution

Step 1. Subtract.

Step 2. Factor by using GCF.

Step 3. Write zero product property.

Step 4. Apply zero product property.

Step 5. Check the obtained solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Probability and Statistics

Mechanics Maths

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solutions.
$24 + x^{2} = 10 x$