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 - Page 775: 18



Work Step by Step

$\dfrac{1}{2}y^{2}=y+\dfrac{1}{2}$ Multiply the whole equation by $2$ to avoid working with fractions: $2\Big(\dfrac{1}{2}y^{2}=y+\dfrac{1}{2}\Big)$ $y^{2}=2y+1$ Take all the terms on the right to the left side of the equation: $y^{2}-2y-1=0$ Use the quadratic formula to solve this equation. The formula is $y=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For this equation, $a=1$, $b=-2$ and $c=-1$ Substitute: $y=\dfrac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(-1)}}{2(1)}=\dfrac{2\pm\sqrt{4+4}}{2}=...$ $...=\dfrac{2\pm\sqrt{8}}{2}=\dfrac{2\pm2\sqrt{2}}{2}=1\pm\sqrt{2}$
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