Answer: x = 3/2 + i√(-3/2), x = 3/2 - i√3/2
Step-by-step explanation:
4x^2 - 12x + 15 = 0
x^2 - 3x +15/4 = 0
x^2 - 3x + (3/2)^2 = -15/4 + (3/2)^2
x^2 - 3x + 9/4 = -15/4 +9/4
x^2 - 3x + 9/4 = -6/4
x^2 - 3x + 9/4 = -3/2
Rewrite the left side of the equation as a perfect square trinomial:
(x-3/2)^2 = -3/2
x - 3/2 = +/-√(-3/2)
x - 3/2 = +/- i√(3/2)
x = 3/2 +/- i√(3/2)
x = 3/2 + i√3/2, x = 3/2 - i√3/2
