4n2+4n+36=0

Question

4n²+4n+36=0

Answer 1

The follow steps demonstrate how to complete the square to find the solution to the problem

4n² + 4n + 36 = 0                          Given

4n² + 4n= -36                                Subtract 36 from each side

n² + n = -9                                    Divide each side by 4

n² + n + 1/4 = - 9 + 1/4                  Add (b/(2a))² to each side.  (Since b and a are each 4, b/(2a) is 1/2)

n² + n + 1/4 = -35/4                       Simplify the right side

(n + 1/2)² = -35/4                          Factor the left side into the perfect square (variable + b/(2a))

n + 1/2 = +/- sqrt(-35/4)                Take the square root of both sides

n + 1/2 = +/- sqrt(35)/2*i               Simplify the right side

n = -1/2 +/- sqrt(35)/2*i                Subtract 1/2 from each side