Question

Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a.

4x2 - 32x + 16 = 0

Answer 1

4x^2 - 32x + 16 = 0
4(x^2 - 8x + 4) = 0
x^2 - 8x + 4 = 0
x^2 - 8x = -4
x^2 - 8x + 16 = 16 - 4
(x - 4)^2 = 12

Answer 2

To get the 16...


(b/2)^2 = (-8/2)^2 = (-4)^2 = 16

Answer 3

$$
\tt \bf\\
\Large4x2 - 32x + 16 = 0\\
\Large4(x^2 - 8x + 4) = 0\\
\Large4(x^2 + bx + c) = 0\\
\Large\Large\text{Use }
\Large(x+b/2)^2+c-(b/2)^2=0~\text{,with b = -8 and c = 4}\\
\Large\text{So, }(x+b/2)^2=(b/2)^2-c
$$