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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 50 (page 1166)

Solve the quadratic equation using square root property.
$2 d^{2} - 4 = 77$

Short Answer

Expert verified

The solutions are $d = 卤 \frac{9 \sqrt{2}}{2}$ .

Step by step solution

01

Given Information.

The Given equation is $2 d^{2} - 4 = 77$ .

02

Isolate the binomial term.

$2 d^{2} = 77 + 42 d^{2} = 81 d^{2} = \frac{81}{2}$

03

Use the Square Root Property.

$d = 卤 \sqrt{\frac{81}{2}}$

Factor the radical.

$d = 卤 \sqrt{\frac{9 脳 9}{2}} d = 卤 \frac{9}{\sqrt{2}}$

04

Rationalize the denominator.

$d = 卤 \frac{9}{\sqrt{2}} 脳 \frac{\sqrt{2}}{\sqrt{2}} d = 卤 \frac{9 \sqrt{2}}{2}$

Rewrite to show two solutions.

$d = \frac{9 \sqrt{2}}{2}, d = - \frac{9 \sqrt{2}}{2}$

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