Algebra
posted by Alicia on .
Complete the square to obtain exact solutions:
x^2+6x+13 = 0
2x^25x3 = 0

In the first problem, you want to have
x^2 + 6x + 9 on the left side, since that is the perfect square (x+3)^2.
You can make that happen by rewriting the equation as
(x+3)^2 = 4
x +3 = + or 2i
x = 3 +/ 2i
(i is the square root of 1)
Now that you have seen how completing the square works, you should try the second one. I would factor out 2 first to make the perfect square simpler. Start with
x^2 (5/2)x = 3/2 (a)
The perfect square that you need is
x (5/2)x + 25/16 = [x (5/4)]^2
So add 25/16 to both sides of Equation (a)and go from there.