Question

find the solution set.
8x² - 2x = 1
separate the two values with a comma.
enter the correct answer.

Explanation:

Step1: Rewrite to standard quadratic form

$8x^2 - 2x - 1 = 0$

Step2: Apply quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, $a=8$, $b=-2$, $c=-1$.
First calculate discriminant:
$\Delta = (-2)^2 - 4\times8\times(-1) = 4 + 32 = 36$
Then compute roots:
$x=\frac{-(-2)\pm\sqrt{36}}{2\times8}=\frac{2\pm6}{16}$

Step3: Calculate two root values

First root: $x=\frac{2+6}{16}=\frac{8}{16}=\frac{1}{2}$
Second root: $x=\frac{2-6}{16}=\frac{-4}{16}=-\frac{1}{4}$

Answer:

$\frac{1}{2}, -\frac{1}{4}$