Question

Solve the equation x^(2)-x=5x-25 over the complex numbers. Simplify the answer. Show your work.

Answer 1

Answer: x = 3 + 4i   and   x = 3 - 4i

where i = sqrt(-1)

========================================================

Work Shown:

First get everything to one side

x^2-x = 5x-25

x^2-x-5x+25 = 0

x^2-6x+25 = 0

Now use the quadratic formula. We'll plug in a = 1, b = -6, c = 25

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-6)\pm\sqrt{(-6)^2-4(1)(25)}}{2(1)}\\\\x = \frac{6\pm\sqrt{-64}}{2}\\\\x = \frac{6\pm8i}{2} \ \ \text{ where } i = \sqrt{-1}\\\\x = \frac{2(3\pm4i)}{2}\\\\x = 3\pm4i\\\\x = 3+4i \ \text{ or } \ x = 3-4i$