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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 423. (page 982)

Solve by completing the square.
$a^{2} = 3 a + 8$

Short Answer

Expert verified

The solution is $a = 卤 \frac{\sqrt{41}}{2} + \frac{3}{2}$ .

Step by step solution

01

Step 1. Given information.

The given equation is $a^{2} = 3 a + 8$ .

02

Step 2. Simplify the equation.

$\begin{array}{rcl} a^{2} & = & 3 a + 8 \\ a^{2} - 3 a & = & 8 \\ a^{2} - 2 路 a 路 \frac{3}{2} & = & 8 \\ a^{2} - 2 路 a 路 \frac{3}{2} + \frac{9}{4} & = & 8 + \frac{9}{4} 鈰� 鈰� (a d d \frac{9}{4} o n b o t h s i d e s) \\ a^{2} - 2 路 a 路 \frac{3}{2} + {(\frac{3}{2})}^{2} & = & \frac{8 脳 4 + 9}{4} \\ {(a - \frac{3}{2})}^{2} & = & \frac{41}{4} \\ a - \frac{3}{2} & = & 卤 \sqrt{\frac{41}{4}} \\ a - \frac{3}{2} & = & 卤 \frac{\sqrt{41}}{2} \\ a & = & 卤 \frac{\sqrt{41}}{2} + \frac{3}{2} \end{array}$

03

Step 3. Simplified answer.

Hence, the required solution is $a = 卤 \frac{\sqrt{41}}{2} + \frac{3}{2}$ .

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