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Q69.

Expert-verified

Pre-algebra

Found in: Page 481

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

Solve ${(x - 2)}^{2} + 1 = 37$ . Describe the steps you use.

The solution of equation is $x = 8, - 4$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The given equation is ${(x - 2)}^{2} + 1 = 37$ .

Step 2. Calculation.

The expression can be solved as

$\begin{matrix} {(x - 2)}^{2} + 1 = 37 \\ {(x - 2)}^{2} = 37 - 1 \\ x^{2} + 4 - 4 x = 36 \\ x^{2} - 4 x - 32 = 0 \end{matrix}$

On further simplification,

$\begin{array}{c} x^{2} - 8 x + 4 x - 32 = 0 \\ x (x - 8) + 4 (x - 8) = 0 \\ (x - 8) (x + 4) = 0 \\ x = 8, - 4 \end{array}$

Step 3. Conclusion.

The solution of equation is $x = 8, - 4$ .

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