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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 257 (page 1236)

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

Short Answer

Expert verified

The solutions are $a = \frac{- \sqrt{41} + 3}{2}, \frac{\sqrt{41} + 3}{2}$

Step by step solution

01

Given Information.

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

02

Isolate the variable terms on one side and the constant terms on the other.The variable terms are on the left side.

$a^{2} - 3 a = 8$

The coefficient of $a$ is $- 3$

So , $b = - 3$

03

Find 12b2and add to the both sides of equation.

$= {(\frac{1}{2} (- 3))}^{2} = {(\frac{- 3}{2})}^{2} = \frac{9}{4}$

Add $\frac{9}{4}$ on both side of equation

$a^{2} - 3 a + \frac{9}{4} = 8 + \frac{9}{4} a^{2} - 3 a + \frac{9}{4} = \frac{41}{4}$

04

Factor the perfect square trinomial as a binomial square

${(a - \frac{3}{2})}^{2} = \frac{41}{4}$

Use square root property

$(a - \frac{3}{2}) = 卤 \sqrt{\frac{41}{4}} a = 卤 \frac{\sqrt{41}}{2} + \frac{3}{2} a = \frac{- \sqrt{41} + 3}{2}, \frac{\sqrt{41} + 3}{2}$

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