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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 94 E (page 1069)

Solve quadratic equations of the form $x^{2} + b x + c = 0$ by completing the square.
In the following exercises , solve by completing the square.
$y^{2} - 14 = 6 y$

Short Answer

Expert verified

The required value of $y$ is $3 + \sqrt{23}, 3 - \sqrt{23}$

Step by step solution

01

Given information

$y^{2} - 14 = 6 y$

02

Calculation

$y^{2} - 14 = 6 y 鈬� y^{2} - 6 y = 14 鈬� y^{2} - 6 y + (\frac{1}{2} 脳 {(- 6))}^{2} = 14 + 9 鈬� y^{2} - 6 y + 9 = 14 + 9 鈬� {(y - 3)}^{2} = 23 鈬� y - 3 = 卤 \sqrt{23} 鈬� y = 3 卤 \sqrt{23} = 3 + \sqrt{23}, 3 - \sqrt{23}$

The required value of $y$ is $3 + \sqrt{23}, 3 - \sqrt{23}$

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Most popular questions from this chapter

In the following exercises, factor the greatest common factor from each polynomial.

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Multiply: $(a) (6 x + 5) (6 x - 5) (b) (4 p - 7 q) (4 p + 7 q)$

Multiply: $(4 - \sqrt{- 12}) (3 - \sqrt{- 48})$

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