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: 22

Answer

$x = -2.64~~$ or $~~x = 1.14$

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 $c$: $2x^2+3x = 6$ $2x^2+3x-6 = 0$ $a = 2$ $b = 3$ $c = -6$ We can use the quadratic formula to find the solutions of the equation: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ $x = \frac{-(3) \pm \sqrt{(3)^2-(4)(2)(-6)}}{(2)(2)}$ $x = \frac{-3 \pm \sqrt{9+48}}{4}$ $x = \frac{-3 \pm \sqrt{57}}{4}$ $x = \frac{-3 - \sqrt{57}}{4}~~$ or $~~x = \frac{-3 + \sqrt{57}}{4}$ $x = -2.64~~$ or $~~x = 1.14$
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