Question

use the quadratic formula to solve the quadratic equation. (enter your answers as a comma - separated list.) x^2 + 8x + 17 = 0 x =

Explanation:

Step1: Identify coefficients

For the quadratic equation $x^{2}+8x + 17=0$, we have $a = 1$, $b = 8$, $c = 17$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac$. Substitute the values: $\Delta=(8)^{2}-4\times1\times17=64 - 68=-4$.

Step3: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Substitute $a = 1$, $b = 8$, $\Delta=-4$:
\[

$$\begin{align*} x&=\frac{-8\pm\sqrt{-4}}{2\times1}\\ &=\frac{-8\pm2i}{2}\\ &=-4\pm i \end{align*}$$

\]

Answer:

$-4 + i,-4 - i$