solve the equation for all real and imaginary solutions
(x-3/2)^2-2(x-3/2)+26=0
Solve for (x - 3/2) using the Quadratic Formula:
x - 3/2 = (2 +- sqrt(4 - 104)) 2,
x - 3/2 = (2 +- sqrt(100*-1)) / 2,
= (2 +- 10i) / 2,
= 1 +- 5i,
x = 1 + 3/2 +- 5i,
x = 2/2 + 3/2 +- 5i,
x = 5/2 +- 5i.
x = 5/2 + 5i, and 5/2 - 5i.
CHECK:
(5/2 - 3/2 + 5i)^2 - 2(5/2 - 3/2 + 5i)=
(1 + 5i)^2 - 2(1 + 5i) + 26 =
1 + 10i - 25 - 2 -10i + 26 =
1 - 25 - 2 + 26 = 27 - 27 = 0.