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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 10.11 (page 1160)

Solve $5 r^{2} - 2 = 34$

Short Answer

Expert verified

The solutions are $r = 卤 \frac{6 \sqrt{5}}{5}$ .

Step by step solution

01

Given Information.

The Given equation is $5 r^{2} - 2 = 34$ .

02

Isolate the quadratic term and makes its coefficient one.

$5 r^{2} = 34 + 25 r^{2} = 36$

03

Use the square root property.

$r^{2} = \frac{36}{5} r = 卤 \sqrt{\frac{36}{5}}$

Factor the radical.

$r = 卤 \sqrt{\frac{36}{5}} r = 卤 \sqrt{\frac{6 脳 6}{5}} r = 卤 \frac{6}{\sqrt{5}}$

04

Rationalize the denominator.

$r = 卤 \frac{6}{\sqrt{5}} 脳 \frac{\sqrt{5}}{\sqrt{5}} r = 卤 \frac{6 \sqrt{5}}{5}$

Rewrite to show two solutions.

$r = \frac{6 \sqrt{5}}{5}, r = - \frac{6 \sqrt{5}}{5}$

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