# Algebra Examples

Solve by Completing the Square
Step 1
Subtract from both sides of the equation.
Step 2
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of .
Step 3
Add the term to each side of the equation.
Step 4
Simplify the equation.
Step 4.1
Simplify the left side.
Step 4.1.1
Raise to the power of .
Step 4.2
Simplify the right side.
Step 4.2.1
Simplify .
Step 4.2.1.1
Raise to the power of .
Step 4.2.1.2
Step 5
Factor the perfect trinomial square into .
Step 6
Solve the equation for .
Step 6.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 6.2
Simplify .
Step 6.2.1
Rewrite as .
Step 6.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 6.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 6.3.1
First, use the positive value of the to find the first solution.
Step 6.3.2
Move all terms not containing to the right side of the equation.
Step 6.3.2.1
Subtract from both sides of the equation.
Step 6.3.2.2
Subtract from .
Step 6.3.3
Next, use the negative value of the to find the second solution.
Step 6.3.4
Move all terms not containing to the right side of the equation.
Step 6.3.4.1
Subtract from both sides of the equation.
Step 6.3.4.2
Subtract from .
Step 6.3.5
The complete solution is the result of both the positive and negative portions of the solution.