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 272: 80


$x=\left\{ -3i,3i \right\} $

Work Step by Step

Using $ax^2+bx+c=0,$ the given equation, \begin{align*} x^2+9=0 ,\end{align*} has $a= 1 ,$ $b= 0 ,$ 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{-0\pm\sqrt{0^2-4(1)(9)}}{2(1)} \\\\ x&=\dfrac{\pm\sqrt{-36}}{2} \\\\ x&=\dfrac{\pm\sqrt{-1}\cdot\sqrt{36}}{2} \\\\ x&=\dfrac{\pm\sqrt{-1}\cdot6}{2} \\\\ x&=\dfrac{\pm i\cdot6}{2} \\\\ x&=\pm\dfrac{6i}{2} \\\\ x&=\pm3i .\end{align*} The solutions are $ x=\left\{ -3i,3i \right\} .$
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