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: 12

Answer

$x=\dfrac{5}{2}\pm\dfrac{\sqrt{77}}{2}$

Work Step by Step

$x^{2}-13=5x$ Take the $5x$ to the left side of the equation: $x^{2}-5x-13=0$ 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 $c=-13$ Substitute: $x=\dfrac{-(-5)\pm\sqrt{(-5)^{2}-4(1)(-13)}}{2(1)}=\dfrac{5\pm\sqrt{25+52}}{2}=...$ $...=\dfrac{5\pm\sqrt{77}}{2}=\dfrac{5}{2}\pm\dfrac{\sqrt{77}}{2}$
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