How do you get a perfect binomial?

Question

FOr the equation x^2 (squared) + 12x + C

First how would you solve C, and then how would u get a perfect binomial? Can u explain the steps because we did it in class and i still dont understand?? Thanks.

Answer 1

Assuming you have no coefficient on the x² term you just do the following (called completing the square):

x² + 12x + C

Take half of the coefficient on x (12/2 = 6), and square it (36)... this is your answer for C.
x² + 12x + 36
(x + 6)(x + 6)
(x + 6)² = x² + 12x + C (C = 36)