Elementary Geometry for College Students (7th Edition)

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: 19


$x = 2~~$ or $~~x=5$

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 $c$: $x^2-7x+10 = 0$ $a = 1$ $b = -7$ $c=10$ We can use the quadratic formula to find the solutions of the equation: $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ $x = \frac{-(-7) \pm \sqrt{(-7)^2-(4)(1)(10)}}{(2)(1)}$ $x = \frac{7 \pm \sqrt{49-40}}{2}$ $x = \frac{7 \pm \sqrt{9}}{2}$ $x = \frac{7 \pm 3}{2}$ $x = \frac{7 - 3}{2}~~$ or $~~x = \frac{7 + 3}{2}$ $x = 2~~$ or $~~x=5$
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