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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 250 (page 1236)

In the following exercises, solve by completing the square.
$y^{2} - 16 y = 36$

Short Answer

Expert verified

The solutions are $y = - 2 a n d y = 18 .$

Step by step solution

01

Given information.

Given equation is $y^{2} - 16 y = 36$

02

Make the perfect square.

Add 64 to both sides of the equation.

$y^{2} - 16 y + 64 = 36 + 64 y^{2} - 16 y + 64 = 100$

Writing it as a binomial square.

$y^{2} - 2 脳 y 脳 8 + 8^{2} = 100 {(y - 8)}^{2} = 100$

03

Use the square root property.

$y - 8 = 卤 \sqrt{100} y - 8 = 卤 \sqrt{10^{2}} y - 8 = 卤 10$

The two equations are $y - 8 = 10 a n d y - 8 = - 10 .$

04

Solve both equations for y.

$y - 8 = 10 y = 10 + 8 y = 18 O r y - 8 = - 10 y = - 10 + 8 y = - 2$

Therefore, the solutions are $y = - 2 a n d y = 18 .$

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