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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.416. (page 982)

Solve by completing the square.
$y^{2} - 6 y = 36$

Short Answer

Expert verified

The solution is $y = 卤 3 \sqrt{5} + 3$ .

Step by step solution

01

Step 1. Given information.

The given equation is $y^{2} - 6 y = 36$ .

02

Step 2. Simplify the equation.

$\begin{array}{rcl} y^{2} - 6 y & = & 36 \\ y^{2} - 2 路 y 路 3 & = & 36 \\ y^{2} - 2 路 y 路 3 + 9 & = & 36 + 9 鈰� 鈰� (a d d 9 o n b o t h s i d e s) \\ y^{2} - 2 路 y 路 3 + 3^{2} & = & 45 \\ {(y - 3)}^{2} & = & 45 \\ y - 3 & = & 卤 \sqrt{45} \\ y - 3 & = & 卤 3 \sqrt{5} \\ y & = & 卤 3 \sqrt{5} + 3 \end{array}$

03

Step 3. Simplified answer.

Hence, the required solution is $y = 卤 3 \sqrt{5} + 3$ .

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