Question

Complete the square to obtain exact solutions:

x^2+6x+13 = 0

2x^2-5x-3 = 0

Answer 1

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.