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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 129 (page 1195)

Solve the equation using quadratic formula.
$2 x^{2} + 12 x - 3 = 0$

Short Answer

Expert verified

The roots are $x = \frac{- 6 + \sqrt{42}}{2}, x = \frac{- 6 - \sqrt{42}}{2}$ .

Step by step solution

01

Given Information.

The given equation is $2 x^{2} + 12 x - 3 = 0$ .

02

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

$2 x^{2} + 12 x - 3 = 0$

The equation is in standard form.

So, $a = 2, b = 12, c - 3$ .

03

Substitute the values in quadratic formula.

$x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} x = \frac{- 12 卤 \sqrt{(12)^{2} - 4 (2) (- 3)}}{2 (2)} x = \frac{- 12 卤 \sqrt{144 + 24}}{4} x = \frac{- 12 卤 \sqrt{168}}{4}$

04

Use square root property.

$x = \frac{- 12 卤 4 \sqrt{42}}{4} x = \frac{2 (- 6 卤 \sqrt{42})}{4} x = \frac{- 6 卤 \sqrt{42}}{2}$

Rewrite to show two solutions.

$x = \frac{- 6 + \sqrt{42}}{2}, x = \frac{- 6 - \sqrt{42}}{2}$

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