Question

use the quadratic formula to solve for x.
2x² - 5x - 4 = 0
(if there is more than one solution, separate them with commas.)
x =

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 2\), \(b = -5\), \(c = -4\).

Step2: Recall quadratic formula

Quadratic formula is \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).

Step3: Calculate discriminant

Compute \(b^2 - 4ac = (-5)^2 - 4\times2\times(-4)=25 + 32 = 57\).

Step4: Substitute into formula

Substitute \(a = 2\), \(b = -5\), \(b^2 - 4ac = 57\) into formula:
\(x=\frac{-(-5)\pm\sqrt{57}}{2\times2}=\frac{5\pm\sqrt{57}}{4}\)

Answer:

\(\frac{5 + \sqrt{57}}{4},\frac{5 - \sqrt{57}}{4}\)