Question

use the quadratic formula to solve for x. 8x^2 + 8x + 1 = 0 (if there is more than one solution, separate them)

Explanation:

Step1: Identify coefficients

For the quadratic equation $8x^{2}+8x + 1=0$, we have $a = 8$, $b = 8$, $c = 1$.

Step2: Write quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.

Step3: Calculate discriminant

First, calculate $b^{2}-4ac$. Substitute $a = 8$, $b = 8$, $c = 1$ into it: $b^{2}-4ac=(8)^{2}-4\times8\times1=64 - 32=32$.

Step4: Substitute values into formula

$x=\frac{-8\pm\sqrt{32}}{2\times8}=\frac{-8\pm4\sqrt{2}}{16}=\frac{-2\pm\sqrt{2}}{4}$.

Answer:

$x=\frac{-2 + \sqrt{2}}{4},\frac{-2-\sqrt{2}}{4}$