SOLUTION: solve over the set of complex numbers (x+5)^2=-36 (given) if I work it out I get x^2-10x+61=0 but now what, it won't foil, x^2-10x+25=-36 x^2-10x+25= -61+25 completing t

Question 695868: solve over the set of complex numbers
(x+5)^2=-36 (given)
if I work it out I get x^2-10x+61=0
but now what, it won't foil,
x^2-10x+25=-36
x^2-10x+25= -61+25 completing the square gets me right back where I started...
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
To solve a quadratic equation for complex solutions, you work just as you do for real solutions,
except that you go further than the point where you would say the equation has no real solutions,
because a negative number cannot be the square of a real number,
but it is the square of a complex number.

<-->
The only real (and complex) numbers that squared equal are and
The only complex numbers that squared equal are and
So, the only complex numbers that squared equal are and .
So, either <--> ,
or <-->
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