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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 78 E (page 885)

In the following exercises, solve by completing the square.
$y^{2} - 2 y = 8$

Short Answer

Expert verified

The solution is $y = - 2, y = 4$

Step by step solution

01

Step 1. Given information

Equation: $y^{2} - 2 y = 8$

02

Step 2. Calculation

We have,

$y^{2} - 2 y = 8$

$y^{2} - 2 y + {(\frac{1}{2} \cdot (- 2))}^{2} = 8 + {(\frac{1}{2} \cdot (- 2))}^{2}$

$y^{2} - 2 y + 1 = 8 + 1$

${(y - 1)}^{2} = 9$

$\sqrt{{(y - 1)}^{2}} = \sqrt{9}$

$y - 1 = \pm 3$

$y - 1 + 1 = - 3 + 1, y - 1 + 1 = 3 + 1$

$y = - 2, y = 4$

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