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 245: 12

Answer

$x = -2$ or $x = -6$

Work Step by Step

The quadratic formula is given as $x = \dfrac{-b ± \sqrt {b^2 - 4ac}}{2a}$, where $a$ is the coefficient of the $x^2$ term, $b$ is the coefficient of the $x$-term, and $c$ is the constant term. Plug in the values from this exercise into this formula: $x = \dfrac{-8 ± \sqrt {8^2 - 4(1)(12)}}{2(1)}$ Evaluate the exponent first: $x = \dfrac{-8 ± \sqrt {64 - 4(1)(12)}}{2(1)}$ $x = \dfrac{-8 ± \sqrt {64 - 48}}{2}$ Simplify the radicand: $x = \dfrac{-8 ± \sqrt {16}}{2}$ Take the square root: $x = \dfrac{-8 ± 4}{2}$ Add or subtract terms in the numerator: $x = \dfrac{-4}{2}\quad$ or $\quad x = \dfrac{-12}{2}$ Simplify the fractions: $x = -2$ or $x = -6$
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