Solving Quadratic Equations by Completing the Square
There are some equations where the solutions are rational numbers, and the
equation
can be solved by factoring.
In the next example the solutions are irrational
numbers, and factoring will not work.
Example 1
A quadratic equation with irrational solutions
Solve x^{2}  3x  6 = 0 by completing the square.
Solution
Because a = 1, we first get the x^{2} and x terms on the lefthand side:
x^{2}  3x  6 
= 0 

x^{2}  3x 
= 6 
Add 6 to each side. 








Evenroot property 
x 

Add
to each side.

x 


The solution set is
.
