Answer: x = 3 + 4i and x = 3 - 4i
where i = sqrt(-1)
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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
[tex]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\\\\[/tex]
