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 $v = \frac{9}{2} \pm \frac{\sqrt{89}}{2}$ .

Step by step solution

Given Information

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

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.

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

Factor the perfect square trinomial as a binomial square.

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

Use the square root property.

$v - \frac{9}{2} = \sqrt{\frac{89}{4}} v - \frac{9}{2} = \pm \sqrt{\frac{89}{2 \times 2}} v - \frac{9}{2} = \pm \frac{\sqrt{89}}{2}$

Solve for v.

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

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

Short Answer

Step by step solution

Given Information

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

Factor the perfect square trinomial as a binomial square.

Solve for v.

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Solve the equation by completing square method. v2=9v+2

Short Answer

Step by step solution

Given Information

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

Factor the perfect square trinomial as a binomial square.

Solve for v.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

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