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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 113 (page 1195)

Solve the equation using quadratic formula.
$v (v + 5) - 10 = 0$

Short Answer

Expert verified

The roots are $v = \frac{- 5 + \sqrt{65}}{2}, v = \frac{- 5 - \sqrt{65}}{2}$ .

Step by step solution

01

Given Information.

The given equation is $v (v + 5) - 10 = 0$

02

Write the quadratic equation in standard form and identify a,b,c.

$v (v + 5) - 10 = 0$

Use distributive property to expand.

$v^{2} + 5 v - 10 = 0$

Here,

$a = 1, b = 5, c = - 10$ .

03

Substitute the values in quadratic formula.

$v = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} v = \frac{- 5 卤 \sqrt{5^{2} - 4 (1) (- 10)}}{2 (1)} v = \frac{- 5 卤 \sqrt{25 + 40}}{2} v = \frac{- 5 卤 \sqrt{65}}{2}$

04

Rewrite to show two solutions.

$v_{1} = \frac{- 5 + \sqrt{65}}{2} v_{2} = \frac{- 5 - \sqrt{65}}{2}$

Thus, the roots are $\frac{- 5 + \sqrt{65}}{2}, \frac{- 5 - \sqrt{65}}{2}$ .

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Most popular questions from this chapter

Solve the quadratic equation using square root property.

$(b - 1)^{2} - 9 = 39$

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