SOLUTION: The solutions to 2x^2 - 10x + 13 = -17x^2 - 14x - 28 are a+bi and a-bi, where a and b are positive. What is a + b?

Question 1209257: The solutions to
2x^2 - 10x + 13 = -17x^2 - 14x - 28
are a+bi and a-bi, where a and b are positive. What is a + b?
Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!

Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

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

rearranges to

after getting everything to one side.

Compare with to get these values
a = 19, b = 4, c = 41

Plug them into the quadratic formula

to generate these roots
or
I'll let the student handle the scratch work.

Those roots are of the form p+qi and p-qi where

So,

There's not much else we can do to simplify.

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