Question

use the quadratic formula to solve the equation.
$5x^2 - x + 2 = 0$
$x = \square$
(type an exact answer, using radicals and $i$ as needed. use a comma to se

Explanation:

Step1: Identify a, b, c values

For $5x^2 - x + 2 = 0$, $a=5$, $b=-1$, $c=2$

Step2: Recall quadratic formula

$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

Step3: Compute discriminant

$b^2-4ac=(-1)^2-4(5)(2)=1-40=-39$

Step4: Substitute into formula

$$x=\frac{-(-1)\pm\sqrt{-39}}{2(5)}=\frac{1\pm i\sqrt{39}}{10}$$

Answer:

$\frac{1+i\sqrt{39}}{10}, \frac{1-i\sqrt{39}}{10}$