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 the quadratic equation $2x^{2}+5x - 4=0$, we have $a = 2$, $b = 5$, $c=-4$.

Step2: Write quadratic formula

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

Step3: Substitute values

Substitute $a = 2$, $b = 5$, $c=-4$ into the formula:
\[

$$\begin{align*} x&=\frac{-5\pm\sqrt{5^{2}-4\times2\times(-4)}}{2\times2}\\ &=\frac{-5\pm\sqrt{25 + 32}}{4}\\ &=\frac{-5\pm\sqrt{57}}{4} \end{align*}$$

\]

Answer:

$x=\frac{-5+\sqrt{57}}{4},\frac{-5 - \sqrt{57}}{4}$