How to solve an equation using completing the square method? The equation is 4x^2-12x+21=0?

4x² - 12x + 21 = 0

4[x² - 3x] + 21 = 0

4[x² - 3x + (3/2)²] - 4(3/2)² + 21 = 0

4[x - (3/2)]² + 12 = 0

4[x - (3/2)]² = -12

[x - (3/2)]² = -3

x - (3/2) = √(-3) or x - (3/2) = -√(-3)

x = (3/2) + √3 i or x = (3/2) - √3 i

x = (3 + 2√3 i)/2 or x = (3 - 2√3 i)/2

4 [ x² - 3 x + (3/2)² ] - 4 ( 3/2)² + 21 = 4 [ x - 3/2]² + 12---> x = 3/2 ± i √ 3

4x² - 12x + 21 = 0

isolate the constant
4x² - 12x = -21

divide by the leading coefficient
x² - 3x = -21/4

complete the square
 coefficient of the x term: -3
 divide it in half: -3/2
 square it: (-3/2)² = (3/2)²
 use (3/2)² to complete the square:
x² - 3x + (3/2)² = -21 + (3/2)²
(x - 3/2)² = -21 + 9/4 = -75/4
x - 3/2 = ±√(-75/4) = ±(5√3/2)i
x = 3/2 ± (5√3/2)i