Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 4 - Quadratic Functions and Equations - Chapter Review - Page 271: 62

Answer

$x=3$

Work Step by Step

Using the properties of equality, the given equation, $ x^2=6x-9 ,$ is equivalent to \begin{align*} x^2-6x+9&=0 .\end{align*} Using $ax^2+bx+c=0,$ the equation above has $a= 1 ,$ $b= -6 ,$ and $c= 9 .$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then \begin{align*} x&=\dfrac{-(-6)\pm\sqrt{(-6)^2-4(1)(9)}}{2(1)} \\\\&= \dfrac{6\pm\sqrt{36-36}}{2} \\\\&= \dfrac{6\pm0}{2} \\\\&= \dfrac{6}{2} \\\\&= 3 .\end{align*} The solution is $ x=3 .$
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