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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 45 (page 869)

Solve quadratic equation $36 x^{2} - 24 x + 4 = 81$ using square root property

Short Answer

Expert verified

The values of $x$ are $\frac{11}{6}$ and $- \frac{7}{6}$

Step by step solution

01

Step 1. Given information

The quadratic equation $36 x^{2} - 24 x + 4 = 81$

02

Step 2. Factor the perfect square trinomial

$\Rightarrow {(6 x - 2)}^{2} = 81$

03

Step 3. Use square root property

$\Rightarrow 6 x - 2 = \pm 9$

$\Rightarrow 6 x = 2 \pm 9$

$\Rightarrow x = \frac{11}{6}$ and $x = - \frac{7}{6}$

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