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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 49 (page 1166)

Solve the quadratic equation using square root property.
$6 c^{2} + 4 = 29$

Short Answer

Expert verified

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

Step by step solution

01

Given Information.

The Given equation is $6 c^{2} + 4 = 29$ .

02

Isolate the binomial term.

$6 c^{2} = 29 - 46 c^{2} = 25 c^{2} = \frac{25}{6}$

03

Use the Square Root Property.

$c = 卤 \sqrt{\frac{25}{6}}$

Factor the radical.

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

Rationalize the denominator.

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

04

Rewrite to show two solutions.

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

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