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 - Practice and Problem-Solving Exercises - Page 246: 51


$x\approx-1.70 \text{ and } x\approx4.70$

Work Step by Step

In the given equation, \begin{align*} x^2-3x-8=0 ,\end{align*} $a= 1 ,$ $b= -3 ,$ and $c= -8 .$ Using the Quadratic Formula which is given by $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a},$ then \begin{align*}\require{cancel}x&= \dfrac{-(-3)\pm\sqrt{(-3)^2-4(1)(-8)}}{2(1)} \\\\&= \dfrac{3\pm\sqrt{9+32}}{2} \\\\&= \dfrac{3\pm\sqrt{41}}{2} \end{align*} \begin{array}{lcl} &\Rightarrow \dfrac{3-\sqrt{41}}{2} &\text{ OR }& \dfrac{3+\sqrt{41}}{2} \\\\& \approx-1.70 && \approx4.70 \end{array} Hence, the solutions are $ x\approx-1.70 \text{ and } x\approx4.70 .$
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