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: 25

Answer

$x=-2\pm\sqrt{11}$

Work Step by Step

$(x+5)(x-1)=2$ Evaluate the product on the left side of the equation: $x^{2}+4x-5=2$ Take the $2$ to the left side: $x^{2}+4x-5-2=0$ Simplify the equation by combining like terms: $x^{2}+4x-7=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=1$, $b=4$ and $c=-7$ Substitute: $x=\dfrac{-4\pm\sqrt{4^{2}-4(1)(-7)}}{2(1)}=\dfrac{-4\pm\sqrt{16+28}}{2}=...$ $...=\dfrac{-4\pm\sqrt{44}}{2}=\dfrac{-4\pm2\sqrt{11}}{2}=-2\pm\sqrt{11}$
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