Quadratic Equations with Imaginary Solutions
We can get imaginary solutions by completing the square.
Example 1
An equation with imaginary solutions
Find the complex solutions to x^{2}  4x + 12 = 0.
Solution
Because the quadratic polynomial cannot be factored, we solve the equation by
completing the square.
x^{2}  4x + 12 
= 0 
The original equation 
x^{2}  4x 
= 12 
Subtract 12 from each side. 
x^{2}  4x + 4 
= 12 + 4 
Onehalf of 4 is 2, and (2)^{2} = 4. 
(x  2)^{2} 
= 8 

x  2 
= Â± 
Evenroot property 
x 
= 2 Â± i 

x 
=


Check these values in the original equation. The solution set is {}.
