# Complex Numbers

posted by Allie

How do I go about finding the solutions to the following
x^2-6x+25=0

I know the answer is 3-4i and 3+4i
however, I do not know how to go about finding the these solutions
Thanks :)

1. helper

x^2 - 6x + 25 = 0
Subtract 25 from both sides:
x^2 - 6x = -25
x^2 - 6x + 9 = -16
Factor the left hand side:
(x-3)^2 = -16
Take the square root of both sides:
|x - 3| = 4i
Eliminate the absolute value:
x - 3 = -4i or x - 3 = 4i
x = 3 - 4i or x - 3 = 4i
x = 3 - 4i or x = 3 + 4i

2. Allie

Oh thank you so much
i forgot that when you that the square root of a negative you get the complex #

3. helper

You are welcome

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