Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.2 - Solving Quadratic Equations by Completing the Square - Exercise Set: 19

Answer

$x=-\dfrac{5}{2}\pm\dfrac{\sqrt{17}}{2}$

Work Step by Step

$x^{2}+5x=-2$ Take the $-2$ to the left side of the equation: $x^{2}+5x+2=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=5$ and $c=2$ Substitute: $x=\dfrac{-5\pm\sqrt{5^{2}-4(1)(2)}}{2(1)}=\dfrac{-5\pm\sqrt{25-8}}{2}=...$ $...=\dfrac{-5\pm\sqrt{17}}{2}=-\dfrac{5}{2}\pm\dfrac{\sqrt{17}}{2}$
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