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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 46 (page 869)

Solve quadratic equation $64 x^{2} + 144 x + 81 = 25$ using square root property

Short Answer

Expert verified

The values of $x$ are $- \frac{7}{4}$ and $- \frac{1}{2}$

Step by step solution

01

Step 1. Given information

The quadratic equation $64 x^{2} + 144 x + 81 = 25$

02

Step 2. Factor the perfect square trinomial

$\Rightarrow {(8 x + 9)}^{2} = 25$

03

Step 3. Use square root property

$\Rightarrow 8 x + 9 = \pm 5$

$\Rightarrow 8 x = \pm 5 - 9$

$\Rightarrow x = - \frac{7}{4}$ and $x = - \frac{1}{2}$

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