Completing the square: x^2+8x+c and also x^2-16x+c?

Question

Completing the square: x^2+8x+c and also x^2-16x+c?

Answer 1

Greetings,

Recall that (x + a)^2 = x^2 + 2ax + a^2 = x^2 + 2ax + (2a/2)^2

Then the value of c making each a complete square is ...

for x^2 + 8x, 1/2 of 8 is 4, 4 squared is 16, c = 16

for x^2 - 16x, 1/2 of -16 is -8, -8 squared is 64, c = 64

Regards