Find the exact solutions to the quadratic equation in the complex numbers.
-$$x ^ { 2 } - 4 x + 29 = 0$$
A) $4 \pm 10 \mathrm { i }$
B) $2 \pm 5 \mathrm { i }$
C) $- 2 \pm 5 i$
D) $7 , - 3$

Question

Quizplus · Accepted Answer

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For the equation $x^2 - 4x + 29 = 0$, $a = 1$, $b = -4$, and $c = 29$. Plugging these into the formula gives $x = \frac{4 \pm \sqrt{(-4)^2 - 4(1)(29)}}{2(1)} = \frac{4 \pm \sqrt{16 - 116}}{2} = \frac{4 \pm \sqrt{-100}}{2} = 2 \pm 5i$.

Find the Exact Solutions to the Quadratic Equation in the Complex