Answer
The solution set is : $\{\frac{-1 + 3i\sqrt{7}}{8}, \frac{-1 - 3i\sqrt{7}}{8}\}$
Work Step by Step
1. Find the equation in its standard form:
$4x^2 + x + 4 = 0$
2. Now, use the quadratic formula to solve for "x".
$x = \frac{-(1) ± \sqrt{(1)^2 - 4(4)(4)}}{2(4)}$
$x = \frac{-1 ± \sqrt{1 - 64}}{8} = \frac{-1 ± \sqrt{-63}}{8}$
$x = \frac{-1 ± i\sqrt{63}}{8} = \frac{-1 ± i\sqrt{7\times9}}{8}$
$x = \frac{-1 ± 3i\sqrt{7}}{8}$
Therefore, the solution set for this expression is:
$\{\frac{-1 + 3i\sqrt{7}}{8}, \frac{-1 - 3i\sqrt{7}}{8}\}$
