Solve: 4=2x-3x^2 by completing the square

Answer 1

3x² - 2x + 4 = 0

x² - (2/3)x = -4/3 [(1/2)(-2/3)]² = 1/9

x² - (2/3)x + 1/9 = -4/3 + 1/9

(x - 1/3)² = -11/9

x - 1/3 = ± √(-11/9)

x = (1 ± √11 i) / 3

Answer 2

3x² - 2x + 4 = 0 (rearrange the given eqn to this form)

x = (2 +/-sqrt(4 - 4*3*4)) / (2*3) (use the formula to solve for the roots of the quadratic eqn)

x = (1 +/-sqrt(-11))/3 (x has imaginary roots)

x = (1 +/-sqrt(11)*i)/3 (i is the imaginary number sqrt(-1))

hope this helps