To solve quadratic equations like ( ax^2 + bx + c = 0 ) when the answers are complex, follow these simple steps:

1. Find the Discriminant:

   • Use this formula: ( D = b^2 - 4ac ).
   • If ( D < 0 ), it means the solutions will be complex.

2. Use the Quadratic Formula:

   • The solutions can be found using: [ x = \frac{-b \pm \sqrt{D}}{2a} ]

3. Simplify the Square Root:

   • If ( D < 0 ), write ( \sqrt{D} ) as ( i\sqrt{|D|} ).
   • Here, ( i ) stands for the imaginary unit.

4. Write the Complex Solutions:

   • The final answers will look like this: [ x = \frac{-b}{2a} \pm \frac{i\sqrt{|D|}}{2a} ]

By following these steps, you will find two complex solutions that are related to each other, called complex conjugates.