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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 10: Q 222 (page 1235)

Solve quadratic equation using the square root property: $\frac{2}{3} w^{2} - 20 = 30$ .

Short Answer

Expert verified

The required result is $w = \pm 5 \sqrt{3}$

Step by step solution

01

Given information

The given expression is $\frac{2}{3} w^{2} - 20 = 30$

02

Simplifying the equation

Add 20 both side of equation .

$\frac{2}{3} w^{2} = 50$

Simplify further ,

$w^{2} = 75$

03

Use square root property

If $x^{2} = k$ and $k \geq 0$ then , $x = \pm \sqrt{k}$

$75 \geq 0$

$w = \pm \sqrt{75}$

$w = \pm 5 \sqrt{3}$

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