With quadratic equations (ax
^{2} + bx + c = 0), you can solve by completing the square.
Step 1: Make sure that the left side of the equation looks like x^{2} + bx.
Step 2: Add to both sides.
Step 3: Factor the left side as
Step 4: Take the square root and solve.
Solve by completing the square.
x^{2}  2x  3 = 0
Step 1: Make sure that the left side of the equation looks like x^{2} + bx.
To make the left side of the equation look like x
^{2} + bx, add 3 to both sides.
x^{2}  2x  3 
= 
0 



x^{2}  2x 
= 
3 
Step 2: Add to both sides.
Since b=2,
Add 1 to both sides.
x^{2}  2x 
= 
3 



x^{2}  2x + 1 
= 
4 
Step 3: Factor the left side as
In general, an expression of the form can be factored as
The expression
x^{2}  2x + 1 is of this form, with b=2. So, it can be factored as (x1)^{2}.
Rewrite the equation with the left side factored.
(x1)^{2} = 4
Step 4: Take the square root and solve.
x  1 
= 


Take the square root 





x 
= 


Add 1 to both sides 





x = 1+2 or x = 12 Split into + or  





x=3 
or 
x=1 

Simplify 