solve for x and express the roots in simplest a+bi from: (x^2)-6x=-21?

x² - 6x = -21
x² - 6x + 21 = 0
x = {6 ± √[(-6)² - 4(1)(21)] }/2
x = {6 ± √-48}/2
x = {6 ± 4√-3}/2
x = 3 ± 2√-3
x = 3 ± 2i√3

x² - 6x + 21 = 0
x = [ 6 ± √ (36 - 84 ) ] / 2
x = [ 6 ± √ (- 48 ) ] / 2
x = [ 6 ± i 4√3 ] / 2
x = 3 ± i 2√3

x^2 - 6x = -21
x^2 - 3x - 3x = -21
x^2 - 3x - 3x + 9 = -21 + 9
(x^2 - 3x) - (3x - 9) = -12
x(x - 3) - 3(x - 3) = -12
(x - 3)(x - 3) = -12
(x - 3)^2 = -12
x - 3 = ±√(-12)
x - 3 = ±√(2^2 * i^2 * 3)
x = 3 ±2i√3

(3,-3.464i)
(3,3.464i)

(x^2)-6x=-21
x^2-6x+21=0
D=36-4*1*21=-48=48*i^2
x=(6+/- 4i√3)/2=3+/-2i√3

Sure:

x^2-6x+21=0

Quadratic formula yields:

x=3±2i√3