Algebra 2 Common Core

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

Chapter 4 - Quadratic Functions and Equations - 4-7 The Quadratic Formula - Lesson Check - Page 244: 2


$x=\left\{ \dfrac{-3-\sqrt{61}}{2},\dfrac{-3+\sqrt{61}}{2} \right\} $

Work Step by Step

In the given equation, \begin{align*} x^2+3x-13=0 ,\end{align*} $a= 1 ,$ $b= 3 ,$ and $c= -13 .$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then \begin{align*}x&= \dfrac{-3\pm\sqrt{3^2-4(1)(-13)}}{2(1)} \\\\&= \dfrac{-3\pm\sqrt{9+52}}{2} \\\\&= \dfrac{-3\pm\sqrt{61}}{2} .\end{align*} Hence, the solutions are $ x=\left\{ \dfrac{-3-\sqrt{61}}{2},\dfrac{-3+\sqrt{61}}{2} \right\} .$
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