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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.425. (page 983)

Solve by completing the square.
$(u + 8) (u + 4) = 14$

Short Answer

Expert verified

The solution is $u = 卤 3 \sqrt{2} - 6$ .

Step by step solution

01

Step 1. Given information.

The given equation is $(u + 8) (u + 4) = 14$ .

02

Step 2. Simplify the equation.

$\begin{array}{rcl} (u + 8) (u + 4) & = & 14 \\ u (u + 4) + 8 (u + 4) & = & 14 \\ u^{2} + 4 u + 8 u + 32 & = & 14 \\ u^{2} + 12 u + 32 & = & 14 \\ u^{2} + 12 u + 32 - 32 & = & 14 - 32 鈰� 鈰� (s u b t r a c t 32 f r o m b o t h s i d e s) \\ u^{2} + 12 u & = & - 18 \\ u^{2} + 2 路 u 路 6 & = & - 18 \\ u^{2} + 2 路 u 路 6 + 36 & = & - 18 + 36 鈰� 鈰� (a d d 36 o n b o t h s i d e s) \\ u^{2} + 2 路 u 路 6 + 6^{2} & = & 18 \\ {(u + 6)}^{2} & = & 18 \\ u + 6 & = & 卤 \sqrt{18} \\ u + 6 & = & 卤 3 \sqrt{2} \\ u & = & 卤 3 \sqrt{2} - 6 \end{array}$

03

Step 3. Simplified answer.

Hence, the required solution is $u = 卤 3 \sqrt{2} - 6$ .

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