Question

solve the quadratic equation.
-x² - 6x - 25 = 0
write one exact, simplified solution in each box. you can add or remove boxes. if a solution is not a real number, write it in the form a + bi or a - bi, where a and b are real numbers.

Explanation:

Step1: Multiply by -1 to simplify

Multiply the equation \(-x^2 - 6x - 25 = 0\) by \(-1\) to get \(x^2 + 6x + 25 = 0\).

Step2: Use quadratic formula

For a quadratic equation \(ax^2 + bx + c = 0\), the solutions are \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 1\), \(b = 6\), \(c = 25\).
Calculate the discriminant: \(b^2 - 4ac = 6^2 - 4\times1\times25 = 36 - 100 = -64\).
Then \(x=\frac{-6\pm\sqrt{-64}}{2\times1}=\frac{-6\pm8i}{2}=-3\pm4i\).

Answer:

-3 + 4i, -3 - 4i