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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 601 (page 857)

In the following exercises, solve.
$\sqrt{x + 5} + 1 = x$

Short Answer

Expert verified

The solution of the equation is $x = - 1 o r 4$

Step by step solution

01

Step 1. Given Information

We have $\sqrt{x + 5} + 1 = x \sqrt{x + 5} = x - 1$

02

Step 2. Squaring both sides

${(\sqrt{x + 5})}^{2} = {(x - 1)}^{2} x + 5 = {(x - 1)}^{2}$

03

Step 3. Simplify the equation

$x + 5 = x^{2} - 2 x + 1 x^{2} - 3 x - 4 = 0$

04

Step 4. Factorize the equation

$x^{2} - 4 x + x - 4 = 0 x (x - 4) + 1 (x - 4) = 0 (x + 1) (x - 4) = 0 x = - 1, 4$

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Most popular questions from this chapter

In the following exercises, simplify.

(a) $- 9^{\frac{3}{2}}$

(b) $- 9^{- \frac{3}{2}}$

(c) ${(- 9)}^{\frac{3}{2}}$

In the following exercises, use the Product Property to simplify radical expression $\sqrt{27}$ .

Use the Quotient Property to simplify square roots.

(a) $\frac{\sqrt{45 p^{9}}}{\sqrt{5 q^{2}}}$

(b) $\frac{\sqrt[4]{64}}{\sqrt[4]{2}}$

(c) $\frac{\sqrt[5]{128 x^{8}}}{\sqrt[5]{2 x^{2}}}$

Simplify:

$(a) \sqrt{\frac{75}{48}} (b) \sqrt[3]{\frac{54}{250}} (c) \sqrt[4]{\frac{32}{162}}$

Explain why $7 + \sqrt{9}$ is not equal to $\sqrt{7 + 9}$ .

See all solutions

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