Question

solve for x. write both solutions, separated by a comma.
8x² - 2x - 1 = 0
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $8x^2 - 2x - 1 = 0$, $a=8$, $b=-2$, $c=-1$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values:

$$ x=\frac{-(-2)\pm\sqrt{(-2)^2-4(8)(-1)}}{2(8)} $$

Step3: Calculate discriminant

Compute $b^2-4ac$:
$\sqrt{4 + 32}=\sqrt{36}=6$

Step4: Solve for two roots

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

Answer:

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