Question

solve for x. write both solutions, separated by a comma.
4x² + 8x - 5 = 0
enter the correct answer.

Explanation:

Step1: Identify quadratic coefficients

For $4x^2 + 8x - 5 = 0$, $a=4$, $b=8$, $c=-5$

Step2: Apply quadratic formula

Quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute values: $x=\frac{-8\pm\sqrt{8^2-4(4)(-5)}}{2(4)}$

Step3: Calculate discriminant

$\sqrt{64 + 80}=\sqrt{144}=12$

Step4: Compute two solutions

First solution: $x=\frac{-8+12}{8}=\frac{4}{8}=\frac{1}{2}$
Second solution: $x=\frac{-8-12}{8}=\frac{-20}{8}=-\frac{5}{2}$

Answer:

$\frac{1}{2}, -\frac{5}{2}$