How to complete the square
Completing the square refers to the process of rewriting a general quadratic expression into the form of a(x+b)2 + c.For example we are asked to complete the square for 2x2+ 4x + 5. The best way to do this is to expand the expression and compare the coefficients.1:Expansiona(x+b)2 + c = ax2+2abx+ab2+c, notice that the coefficient of x2 is a, the coefficient of x is 2ab and the coefficient of x0 (constant term) is ab2+c. 2:Compare the coefficient. Since the completed square form has to be the same as the original expression, we can see that a = 2, 2ab = 4, and ab2+c = 5. We can then work out b = 1 and c = 3. The answer is therefore 2(x+1)2 + 3. If you want to check this, you can expand this and it will be 2x2+ 4x + 5.
