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: 30

Answer

$x=-\dfrac{9}{2}\pm\dfrac{\sqrt{105}}{2}$

Work Step by Step

$\dfrac{x^{2}}{2}-3=-\dfrac{9}{2}x$ Multiply the whole equation by $2$ to avoid working with fractions: $2\Big(\dfrac{x^{2}}{2}-3=-\dfrac{9}{2}x\Big)$ $x^{2}-6=-9x$ Take the $-9x$ to the left side of the equation: $x^{2}+9x-6=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=1$, $b=9$ and $c=-6$ Substitute: $x=\dfrac{-9\pm\sqrt{9^{2}-4(1)(-6)}}{2(1)}=\dfrac{-9\pm\sqrt{81+24}}{2}=...$ $...=\dfrac{-9\pm\sqrt{105}}{2}=-\dfrac{9}{2}\pm\dfrac{\sqrt{105}}{2}$
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