Question 980627
Because we are dealing with complex numbers, we will need to use the quadratic formula, where a = 1, b = -4, and c = 9, and substitute the letters with the numbers represented by them:


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a)}}}


{{{x = (-(-4) +- sqrt((-4)^2-(4)(1)(9)))/((2)(1))}}} ----->


{{{x = (4 +- sqrt(16-36))/(2) }}} ----->


{{{x = (4 +- sqrt(-20))/(2) }}} ----->


{{{x = (4 +- 2i*sqrt(5))/(2) }}}


Next, factor extract a 2 out of the equation to get rid of the two in our denominator:


{{{x = 2(2 +- i*sqrt(5))/(2) }}} ----->


{{{x = 2 +- i*sqrt(5) }}}, which is our final answer