Example: Solving the quadratic equation.
Suppose a x 2 + b x + c = 0 and a 0 . We first divide by a to get x 2 + b a x + c a = 0 . Then we complete the square and obtain x 2 + b a x + ( b 2 a ) 2 - ( b 2 a ) 2 + c a = 0 . The first three terms factor to give ( x + b 2 a ) 2 = b 2 4 a 2 - c a . Now we take square roots on both sides and get x + b 2 a = ± b 2 4 a 2 - c a 2 . Finally we move the b 2 a to the right and simplify to get the two solutions: x 1 , 2 = - b ± b 2 - 4 a c 2 a