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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. 544 (page 988)

In the following exercises, solve each inequality algebraically and write any solution in interval notation.
$x^{2} - 6 x - 8 鈮� 0$

Short Answer

Expert verified

The required solution is $x 鈭� [3 - \sqrt{7}, 3 + \sqrt{7}]$ .

Step by step solution

01

Step 1. Given information.

We have:

$x^{2} - 6 x - 8 鈮� 0$

02

Step 2. Solve the related quadratic equation

$x^{2} - 6 x - 8 = 0$

For quadratic equation of the form $a x^{2} + b x + c = 0$ , the solutions are:

$x_{1, 鈥� 2} = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} For 鈥� a = 1, 鈥� b = - 6, 鈥� c = - 8 x_{1, 鈥� 2} = \frac{- (- 6) 卤 \sqrt{{(- 6)}^{2} - 4 路鈥� 1 路 (- 8)}}{2 路鈥� 1} x_{1} = \frac{- (- 6) + 2 \sqrt{17}}{2 路鈥� 1}, 鈥� x_{2} = \frac{- (- 6) - 2 \sqrt{17}}{2 路鈥� 1} x = 3 + \sqrt{17}, 鈥� x = 3 - \sqrt{17}$

Hence, the solution is $x 鈭� [3 - \sqrt{7}, 3 + \sqrt{7}]$ .

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