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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 128 (page 898)

In the following exercises, solve by using the Quadratic Formula.
$6 x^{2} + 2 x - 20 = 0$

Short Answer

Expert verified

The solutions of the given equation are $x = \frac{5}{3}$ and $x = - 2$ .

Step by step solution

01

Step 1. Given information.

The given equation is:

$6 x^{2} + 2 x - 20 = 0$

02

Step 2. Substitute the values in Quadratic Formula.

Quadratic Formula for the equation $a x^{2} + b x + c = 0$ is:

$x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

In the given equation, $a = 6, b = 2, c = - 20$ . Substitute these values in Quadratic Formula.

$x = \frac{- 2 卤 \sqrt{2^{2} - 4 (6) (- 20)}}{2 (6)}$

03

Step 3. Simplify the value.

On simplification, we get

$\begin{array}{rcl} x & = & \frac{- 2 卤 \sqrt{4 + 480}}{12} \\ x & = & \frac{- 2 卤 \sqrt{484}}{12} \\ x & = & \frac{- 2 卤 22}{12} \end{array}$

It can be written as:

$x = \frac{- 2 + 22}{12} and x = \frac{- 2 - 22}{12} x = \frac{20}{12} and x = \frac{- 24}{12} x = \frac{5}{3} and x = - 2$

04

Step 4. Conclusion.

The solutions of the given equation are $x = \frac{5}{3}$ and $x = - 2$ .

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