Question

Find all complex solutions of 5x^2+5x+3=0.

(If there is more than one solution, separate them with commas.)
PLEASE NO PHONEY ANSWERS, THE SOLUTION SHOULD LOOK LIKE A FRACTION.

Answer 1

see explanation

Explanation:

5x² + 5x + 3 = 0 ← in standard form

with a = 5 , b = 5 , c = 3

Solve using the quadratic formula

x =
`(-b+/-√(b^2-4ac) )/(2a)`

=
`(-5+/-√(5^2-(4(5)(3)) )/(2(5))`

=
`(-5+/-√(25-60) )/(10)`

=
`(-5+/-√(-35) )/(10)`

=
`(-5+/-√(-1(35)) )/(10)`

=
`(-5+/-i√(35) )/(10)`

Then

x =
`(-5)/(10)` ±
`(1)/(10)` i
`√(35)` , that is

x = -
`(1)/(2)` -
`√(x) (1)/(10)` i
`√(35)` , -
`(1)/(2)` +
`(1)/(10)` i
`√(35)`