Question

use the quadratic formula to solve the equation.\\(x^2 + 6x + 25 = 0\\)\\(\\)\\(\\)the solution(s) is/are \\(x = \square\\).\\((\text{simplify your answer. type an exact answer, using radicals and } i \text{ as needed. use}\\)

Explanation:

Step1: Identify a, b, c values

For $x^2 + 6x + 25 = 0$, $a=1$, $b=6$, $c=25$

Step2: Recall quadratic formula

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

Step3: Calculate discriminant

$\Delta = b^2 - 4ac = 6^2 - 4(1)(25) = 36 - 100 = -64$

Step4: Substitute into formula

$$x = \frac{-6 \pm \sqrt{-64}}{2(1)} = \frac{-6 \pm 8i}{2}$$

Step5: Simplify the expression

$x = -3 \pm 4i$

Answer:

$x = -3 + 4i$ and $x = -3 - 4i$