Question

Solve the equation using the quadratic formula x^2-8x+52=0

Answer 1

The equation x^2 - 8x + 52  =  0

Separate variables and constants aside by subtracting 52 from each side.

x^2 - 8x + 52 - 52  =  0 - 52

x^2 - 8x  =  - 52

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

x^2 - x + (4)^2   =   -52 + 4^2

x^2 - x + (4)^2   =   -52 + 16

(x - 4)^2   =   -36

Take square root on both sides.

(x - 4)   =   √(-36)

(x - 4)   =   6i

x  =  4  ± 6i

Solutions are x  =  4  + 6i and x  =  4  - 6i

Answer :

Solutions are x  =  4  + 6i and x  =  4  - 6i.