Question

use the quadratic formula to solve the equation.
$2x^2 - x + 2 = 0$
$x = \square$
(simplify your answer. type an exact answer, using radicals and $i$ as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed )

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 2\), \(b=-1\), \(c = 2\).

Step2: Apply quadratic formula

Quadratic formula is \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Substitute \(a = 2\), \(b=-1\), \(c = 2\):
\(x=\frac{-(-1)\pm\sqrt{(-1)^2 - 4\times2\times2}}{2\times2}=\frac{1\pm\sqrt{1 - 16}}{4}=\frac{1\pm\sqrt{-15}}{4}\)
Since \(\sqrt{-15}=i\sqrt{15}\), we get \(x=\frac{1\pm i\sqrt{15}}{4}\).

Answer:

\(\frac{1 + i\sqrt{15}}{4},\frac{1 - i\sqrt{15}}{4}\)