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

91影视

Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 11: Q41. (page 729)

_{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 $\sqrt{x + 4} = x 鈭� 8$ .

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

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

When $x = 5$ ,

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

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

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:

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

Step 2. Solve the given equation.

The solution of the given equation is:

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

Therefore, the values $x$ are 12 and 5.

Step 3. Check the solution.

When $x = 12$ ,

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

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

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 $\sqrt{x + 4} = x 鈭� 8$ .

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

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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$x$	1	4	8	12
$y$	2	8	16	24

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

Discrete Mathematics

Decision Maths

Logic and Functions

Theoretical and Mathematical Physics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

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