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:
$4x - 1=0$
$x = \frac{1}{4}$
$2x+ 1 =0$
$x = -\frac{1}{2}$
