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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 9: Q 42. (page 869)

Solve quadratic equation $y^{2} + 12 y + 36 = 32$ using a square root property.

Short Answer

Expert verified

The values of $y$ are $- 6 - 4 \sqrt{2}$ and $- 6 + 4 \sqrt{2}$

Step by step solution

01

Step 1. Write the given information

Consider the quadratic equation $y^{2} + 12 y + 36 = 32$

02

Step 2. Factor the perfect square trinomial

${(y + 6)}^{2} = 32$

03

Step 3. Use square root property

$y + 6 = \pm \sqrt{32}$

$\Rightarrow y = - 6 \pm 4 \sqrt{2}$

$\Rightarrow y = - 6 - 4 \sqrt{2}$ and $y = - 6 + 4 \sqrt{2}$

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