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: 16

Answer

$x=2$ and $x=-10$

Work Step by Step

$\dfrac{1}{8}x^{2}+x=\dfrac{5}{2}$ Multiply the whole equation by $8$ to avoid working with fractions: $8\Big(\dfrac{1}{8}x^{2}+x=\dfrac{5}{2}\Big)$ $x^{2}+8x=20$ Take the $20$ to the left side of the equation: $x^{2}+8x-20=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=8$ and $c=-20$ Substitute: $x=\dfrac{-8\pm\sqrt{8^{2}-4(1)(-20)}}{2(1)}=\dfrac{-8\pm\sqrt{64+80}}{2}=...$ $...=\dfrac{-8\pm\sqrt{144}}{2}=\dfrac{-8\pm12}{2}$ Our two solutions are: $x=\dfrac{-8+12}{2}=2$ $x=\dfrac{-8-12}{2}=-10$
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