Question 1209257
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I'll relabel a+bi and a-bi as p+qi and p-qi respectively.


{{{2x^2 - 10x + 13 = -17x^2 - 14x - 28}}}
rearranges to
{{{19x^2+4x+41 = 0}}} 
after getting everything to one side.



Compare {{{19x^2+4x+41 = 0}}} with {{{ax^2+bx+c = 0}}} to get these values
a = 19, b = 4, c = 41


Plug them into the quadratic formula 
{{{x = (-b +- sqrt(b^2 - 4ac))/(2a)}}} 
to generate these roots
{{{x = -2/19 + (5*sqrt(31)/19)i}}} or {{{x = -2/19 - (5*sqrt(31)/19)i}}}
I'll let the student handle the scratch work.


Those roots are of the form p+qi and p-qi where
{{{matrix(1,3,p = -2/19,"and",q = 5*sqrt(31)/19)}}}


So,
{{{p+q = -2/19 + 5*sqrt(31)/19}}}


{{{p+q = (-2 + 5*sqrt(31))/19}}}
There's not much else we can do to simplify.
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