Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Appendix A - A.5 - The Quadratic Formula and Square Root Properties - Exercises - Page 562: 24

Answer

$x = -0.32~~$ or $~~x = 6.32$

Work Step by Step

A quadratic equation can be written in this form: $ax^2 + bx+c = 0$ where $a,b,$ and $c$ are real numbers and $a \neq 0$ We can determine the values of $a, b,$ and $c$: $x^2-6x -2 = 0$ $a = 1$ $b = -6$ $c = -2$ We can use the quadratic formula to find the solutions of the equation: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ $x = \frac{-(-6) \pm \sqrt{(-6)^2-(4)(1)(-2)}}{(2)(1)}$ $x = \frac{6 \pm \sqrt{36+8}}{2}$ $x = \frac{6 \pm \sqrt{44}}{2}$ $x = \frac{6 - \sqrt{44}}{2}~~$ or $~~x = \frac{6 + \sqrt{44}}{2}$ $x = -0.32~~$ or $~~x = 6.32$
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