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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 85 (page 1181)

Solve the equation by completing square method.
$v^{2} = 9 v + 2$

Short Answer

Expert verified

The solutions are $v = \frac{9}{2} 卤 \frac{\sqrt{89}}{2}$ .

Step by step solution

01

Given Information

The Given equation is $v^{2} = 9 v + 2$ .

02

Isolate the variable terms on one side and the constant terms on the other.

$v^{2} = 9 v + 2 v^{2} - 9 v = 2$

Here, $b = - 9$ .

So, ${(\frac{1}{2} b)}^{2} = {(\frac{1}{2} (- 9))}^{2} = {(\frac{- 9}{2})}^{2} = \frac{81}{4}$ .

Add $\frac{81}{4}$ to both sides of equation.

$v^{2} - 9 v + \frac{81}{4} = 2 + \frac{81}{4} v^{2} - 9 v + \frac{81}{4} = \frac{89}{4}$

03

Factor the perfect square trinomial as a binomial square.

${(v - \frac{9}{2})}^{2} = \frac{89}{4}$

Use the square root property.

$v - \frac{9}{2} = \sqrt{\frac{89}{4}} v - \frac{9}{2} = 卤 \sqrt{\frac{89}{2 脳 2}} v - \frac{9}{2} = 卤 \frac{\sqrt{89}}{2}$

04

Solve for v.

$v = \frac{9}{2} 卤 \frac{\sqrt{89}}{2}$

Rewrite to show two solutions.

$v = \frac{9}{2} + \frac{\sqrt{89}}{2}, v = \frac{9}{2} - \frac{\sqrt{89}}{2}$

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