Question

Complete the square to transform the quadratic equation into the equation form (x – p)2 = q. x2 + 14x + 34 = 5

Answer 1

To complete the square, the constant term on the left (now 34) needs to be (14/2)² = 49, so we need to add (49 -34) = 15 to the equation.
x² +14x +34 +15 = 5 +15
x² +14x +49 = 20
(x +7)² = 20 . . . . . . . . . p = -7, q = 20