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 8.1 - The Square Root Property and Completing the Square - Exercise Set - Page 596: 115

Answer

$x = \frac{1}{4}$ $x = -\frac{1}{2}$

Work Step by Step

$8x^2 + 2x - 1 = 0$ is in the form $ax^2+bx+c$. To solve by factoring: Find two First terms whose product is $ax^2$: $(4x +$ __ $)$$(2x+$ __ $)$ Find two Last terms whose product is $c$: $(4x + 1 )(2x+ (-1) )$ combination 1 $(4x - 1 )(2x+ 1 )$ combination 2 Check for combination 1: $(4x + 1 )(2x+ (-1) )$ $(4x⋅2x) +(-4x⋅-1) +(2x⋅1) -1$ $8x^2+6x-1$ Check for combination 2: $(4x - 1 )(2x+ 1 )$ $(4x⋅2x) +(-1⋅2x) +(4x⋅1) -1$ $8x^2 +2x -1$ Thus, the factors are: $4x - 1=0$ $x = \frac{1}{4}$ $2x+ 1 =0$ $x = -\frac{1}{2}$
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