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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 229. (page 1236)

In the following exercises, solve using the Square Root Property.
${(x - \frac{1}{4})}^{2} = \frac{3}{16}$

Short Answer

Expert verified

The required answer is $x = \frac{\sqrt{3}}{4} + \frac{1}{4} and x = - \frac{\sqrt{3}}{4} + \frac{1}{4}$ .

Step by step solution

01

Step 1. Given information.

The given quadratic equation is:

${(x - \frac{1}{4})}^{2} = \frac{3}{16}$

02

Step 2. Solve using the quadratic equation by using Square Root Property.

{(x - \frac{1}{4})}^{2} = \frac{3}{16}

Use Square Root Property,

$x - \frac{1}{4} = 卤 \sqrt{\frac{3}{16}}$

Simplify the radical,

$x - \frac{1}{4} = 卤 \frac{\sqrt{3}}{\sqrt{16}} x - \frac{1}{4} = 卤 \frac{\sqrt{3}}{4}$

Write as two equations and solve,

$x - \frac{1}{4} = \frac{\sqrt{3}}{4} and x - \frac{1}{4} = - \frac{\sqrt{3}}{4} x = \frac{\sqrt{3}}{4} + \frac{1}{4} and x = - \frac{\sqrt{3}}{4} + \frac{1}{4}$

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