Solving Quadratics With Complex Solutions│Please Help!

Question

Guy is trying to solve the equation x² - 6x + 12 = 0. He knows that the solutions are x² = -1 are ± i, but he is not sure how to use the information to solve for x in the equation.

Here is Guy's work:

x² - 6x + 12 = 0

x² - 6x = -12

x² - 6x + 9 = -12 + 9

(x - 3)² = - 3

Show how Guy can finish his work using complex numbers.

Answer 1

x^2 -6x+12= 0

x^2-6x+9 = -3

x-3= +/-sqr(-3) = +/-isqr3

x= 3+isqr3 or 3-isqr3

where i= the square root of negative one, which is not a real number, it's imaginary

i^2 =-1

any real number squared will be positive, never negative

Answer 2

See the video.