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

For $ax^2+bx+c=0$, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. Here $a=8$, $b=-2$, $c=-1$.
$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(8)(-1)}}{2(8)}$

Step3: Simplify discriminant

$\sqrt{4 + 32}=\sqrt{36}=6$

Step4: Calculate two solutions

$x_1=\frac{2+6}{16}=\frac{8}{16}=\frac{1}{2}$, $x_2=\frac{2-6}{16}=\frac{-4}{16}=-\frac{1}{4}$

Answer:

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