I'll show you an example and then you can use this method to solve your questions.
Example: Find the roots of 2x² + 16x + 20 by completing the square.
Completing the square means we want to make a perfect square as we do this.
We'll solve for it using the equation
2x² + 16x + 20 = 0
First things first though: simplify the numbers if you can! 2 goes into everything, so it reduces to just:
x² + 8x + 10 = 0
I start by moving the constant (third) term to the other side:
x² + 8x = -10
Now I want the left hand side to become a perfect square. The way I do that is by taking half the co-efficient of the x term (that is, one half of 8, which is 4) and then squaring that (to make 16). I add this to both sides of the equation:
x² + 8x + 16 = -10 + 16
The left hand side is now a perfect square. It's the perfect square of x and half of +8 (which is 4). So I can re-write this as:
(x + 4)² = 6
Now I take the square root of both sides. That just cancels out the squared on the left side. Remember that there is both a positive and negative square root!
x + 4 = ±√6
I solve for x:
x = ±√6 - 4
So this is actually two numbers (because of that ± sign). The two roots are:
x = √6 - 4
Now my example is done. I hope you can see how to do your problems now, step by step.
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.