TUTORIALS:

Quadratic Equations with Imaginary Solutions
Example
Solve using the quadratic formula: 2x^{2} + 7 = 3x
Solution
Step 1 
Write the quadratic equation in standard form.
Subtract 3x from both sides of the equation. 
2x^{2}  3x + 7 = 0 
Step 2 
Identify the values of a, b, and c.
a = 2, b = 3, c = 7 

Step 3 
Substitute the values of a, b, and c
into the quadratic formula. 


Substitute 2 for a, 3 for b, and 7 for c. 

Step 4 
Simplify.
Simplify the radicand and the
denominator. 


Use
to simplify the
square root.



Write the final answer in the form a + bi. 

Step 5 
Check each solution.
We leave the check to you. 

So, the solutions of 2x^{2} + 7 = 3x are
Notice that the solutions are complex conjugates.
