Question 176614
If {{{x = 4 + i}}} then {{{x - (4 + i)}}} is a factor of the quadratic.  Similarly, {{{x - (4 - i)}}} is a factor of the quadratic and we can say:


{{{(x - (4 + i))(x - (4 - i)) = 0}}}.


Just multiply the two factors to get back to the original quadratic.  Hints: Treat these two factors as binomials with {{{x}}} being one term and {{{4 +- i}}} as the other term.  Remember that multiplying a conjugate pair results in the difference of two squares, that is:  {{{(a + b)(a - b) = a^2 - b^2}}}.  Therefore {{{(4 + i)(4 - i) = 16 - (-1) = 17}}}