Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 8 - Section 8.2 - The Quadratic Formula - Exercise Set - Page 609: 75


$x=1$ or $x=-3$

Work Step by Step

If $|x| = c$, then $x = c$ or $x = -c. (c>0)$ $x^2+2x=3$ (equation 1) or $x^2+2x=-3$ (equation 2) Solve using the quadratic formula $x=\frac{−b±\sqrt{b^2−4ac}}{2a}$ Equation 1: $x^2+2x=3$ Subtract $3$ to both sides: $x^2+2x-3=3-3$ $x^2+2x-3=0$ $a=1$, $b=2$, $c=-3$ $x=\frac{−2±\sqrt{2^2−(4⋅1⋅-3)}}{2⋅1}$ $x=\frac{−2±\sqrt{4−(-12)}}{2}$ $x=\frac{−2±\sqrt{16}}{2}$ $x=\frac{−2±4}{2}$ $x=1$ or $x=-3$ Equation 2: $x^2+2x=-3$ Add $3$ to both sides: $x^2+2x+3=-3+3$ $x^2+2x+3=0$ $a=1$, $b=2$, $c=3$ $x=\frac{−2±\sqrt{2^2−(4⋅1⋅3)}}{2⋅1}$ $x=\frac{−2±\sqrt{4−(12)}}{2}$ $x=\frac{−2±\sqrt{-8}}{2}$ (no real solution since the discriminant is negative)
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