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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 41 (page 869)

Solve quadratic equation $x^{2} - 6 x + 9 = 12$ using square root property

Short Answer

Expert verified

The values of $x$ are $3 + 2 \sqrt{3}$ and $3 - 2 \sqrt{3}$ .

Step by step solution

01

Step 1. Given information

The quadratic equation $x^{2} - 6 x + 9 = 12$

02

Step 2. Factor the perfect square trinomial

$\Rightarrow {(x - 3)}^{2} = 12$

03

Step 3. Use square root property

$\Rightarrow x - 3 = \pm 2 \sqrt{3}$

$\Rightarrow x = 3 \pm 2 \sqrt{3}$

$\Rightarrow x = 3 + 2 \sqrt{3}$ and $x = 3 - 2 \sqrt{3}$

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