Question

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

Answer 1

Answer:

see explanation

Step-by-step explanation:

5x² + 5x + 3 = 0 ← in standard form

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

Solve using the quadratic formula

x = $\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

  = $\frac{-5+/-\sqrt{5^2-(4(5)(3)} }{2(5)}$

  = $\frac{-5+/-\sqrt{25-60} }{10}$

  = $\frac{-5+/-\sqrt{-35} }{10}$

  = $\frac{-5+/-\sqrt{-1(35)} }{10}$

 = $\frac{-5+/-i\sqrt{35} }{10}$

Then

x = $\frac{-5}{10}$ ± $\frac{1}{10}$ i$\sqrt{35}$ , that is

x = - $\frac{1}{2}$ - $\sqrt{x} \frac{1}{10}$ i$\sqrt{35}$ , - $\frac{1}{2}$ + $\frac{1}{10}$ i$\sqrt{35}$