Question

Complete the square. 4x^2+24x+29
I completely forgot how to do this.

Answer 1

(24/2)^2

Answer 2

\[\Large ax ^{2} + bx + c = a(x + d)^{2} + e\]

The d can be quickly found by: b/2a

Answer 3

a = 4, b = 24, c = 29
d = b/2a = 24 / 8 = 3
So 4x^2 + 24x + 29 = 4(x + 3)^2 + e
find e.

Answer 4

4x^2 + 24x + 29 = 4(x + 3)^2 + e = 4(x^2 + 6x + 9) + e
4x^2 + 24x + 29 = 4x^2 + 24x + 36 + e
29 = 36 + e
e = -7
4x^2 + 24x + 29 = 4(x + 3)^2 - 7