Q41. Solve each equation. Check your ... [FREE SOLUTION]

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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 10: Q41. (page 658)

Solve each equation. Check your solution.
$\sqrt{x + 4} = x 鈭� 8$

Short Answer

Expert verified

The solution of the given equation is $x = 12$ .

Check:

When $x = 12$ ,

Substitute 12 for x in the given equation $\sqrt{x + 4} = x 鈭� 8$ .

$\sqrt{x + 4} = x 鈭� 8 \sqrt{12 + 4} \underset{炉}{\underset{炉}{?}} 12 鈭� 8 \sqrt{16} \underset{炉}{\underset{炉}{?}} 4 4 = 4$

Therefore, $x = 12$ is the solution of the given equation $\sqrt{x + 4} = x 鈭� 8$ .

When $x = 5$ ,

Substitute 5 for x in the given equation $\sqrt{x + 4} = x 鈭� 8$ .

$\sqrt{x + 4} = x 鈭� 8 \sqrt{5 + 4} \underset{炉}{\underset{炉}{?}} 5 鈭� 8 \sqrt{9} \underset{炉}{\underset{炉}{?}} 鈭� 3 3 鈮� 鈭� 3$

Therefore, $x = 5$ is not the solution of the given equation $\sqrt{x + 4} = x 鈭� 8$ .

Step by step solution

Step 1. Rewrite the given equation.

The given equation can be written as:

$\sqrt{x + 4} = x 鈭� 8 {(\sqrt{x + 4})}^{2} = {(x 鈭� 8)}^{2} (squaringbothsides) x + 4 = {(x 鈭� 8)}^{2} x + 4 = x^{2} 鈭� 2 (x) (8) + 8^{2} (鈭� {(a 鈭� b)}^{2} = a^{2} 鈭� 2 a b + b^{2}) x + 4 = x^{2} 鈭� 16 x + 64$

Step 2. Solve the given equation.

The solution of the given equation is:

$x + 4 = x^{2} 鈭� 16 x + 64 0 = x^{2} 鈭� 16 x 鈭� x + 64 鈭� 4 0 = x^{2} 鈭� 17 x + 60 0 = x^{2} 鈭� 12 x 鈭� 5 x + 60 x^{2} 鈭� 12 x 鈭� 5 x + 60 = 0 x (x 鈭� 12) 鈭� 5 (x 鈭� 12) = 0 (x 鈭� 12) (x 鈭� 5) = 0 x 鈭� 12 = 0 or x 鈭� 5 = 0 x = 12 or x = 5$

Therefore, the values x are 12 and 5.

Step 3. Check the solution.

When $x = 12$ ,

Substitute 12 for x in the given equation $\sqrt{x + 4} = x 鈭� 8$ .

$\sqrt{x + 4} = x 鈭� 8 \sqrt{12 + 4} \underset{炉}{\underset{炉}{?}} 12 鈭� 8 \sqrt{16} \underset{炉}{\underset{炉}{?}} 4 4 = 4$

Therefore, $x = 12$ is the solution of the given equation $\sqrt{x + 4} = x 鈭� 8$ .

When $x = 5$ ,

Substitute 5 for x in the given equation $\sqrt{x + 4} = x 鈭� 8$ .

$\sqrt{x + 4} = x 鈭� 8 \sqrt{5 + 4} \underset{炉}{\underset{炉}{?}} 5 鈭� 8 \sqrt{9} \underset{炉}{\underset{炉}{?}} 鈭� 3 3 鈮� 鈭� 3$

Therefore, $x = 5$ is not the solution of the given equation $\sqrt{x + 4} = x 鈭� 8$ .

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91影视

Solve each equation. Check your solution.
$\sqrt{x + 4} = x 鈭� 8$

Short Answer

Step by step solution

Step 1. Rewrite the given equation.

Step 2. Solve the given equation.

Step 3. Check the solution.

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91影视

Solve each equation. Check your solution.x+4=x鈭�8

Short Answer

Step by step solution

Step 1. Rewrite the given equation.

Step 2. Solve the given equation.

Step 3. Check the solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Probability and Statistics

Decision Maths

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve each equation. Check your solution.
$\sqrt{x + 4} = x 鈭� 8$