Question

complete the square to express f(x)=12x^2+24x+48.

Answer 1

Let us assume f(x) = 12x² +24x + 48 = 0.

12x² +24x + 48 = 0

Divide each side by 12.

x² +2x + 4 = 0

Separate variables and constants aside by subtracting 4 from each side.

x² +2x = -4

To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

Add 1 to each side.

x² +2x +1= -4+1

(x +1)² = -3

(x +1)² = i²3   (i² = -1)

Take square root both sides.

x +1 = ± isqrt(3)

Subtract 1 from each side.

x = -1 ± isqrt(3).