# Algebra Examples

Solve by Completing the Square
Step 1
Add to both sides of the equation.
Step 2
Divide each term in by and simplify.
Step 2.1
Divide each term in by .
Step 2.2
Simplify the left side.
Step 2.2.1
Simplify each term.
Step 2.2.1.1
Cancel the common factor of .
Step 2.2.1.1.1
Cancel the common factor.
Step 2.2.1.1.2
Divide by .
Step 2.2.1.2
Cancel the common factor of and .
Step 2.2.1.2.1
Factor out of .
Step 2.2.1.2.2
Cancel the common factors.
Step 2.2.1.2.2.1
Factor out of .
Step 2.2.1.2.2.2
Cancel the common factor.
Step 2.2.1.2.2.3
Rewrite the expression.
Step 2.2.1.2.2.4
Divide by .
Step 2.3
Simplify the right side.
Step 2.3.1
Divide by .
Step 3
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 4
Add the term to each side of the equation.
Step 5
Simplify the equation.
Step 5.1
Simplify the left side.
Step 5.1.1
Raise to the power of .
Step 5.2
Simplify the right side.
Step 5.2.1
Simplify .
Step 5.2.1.1
Raise to the power of .
Step 5.2.1.2
Step 6
Factor the perfect trinomial square into .
Step 7
Solve the equation for .
Step 7.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 7.2
Simplify .
Step 7.2.1
Rewrite as .
Step 7.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 7.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 7.3.1
First, use the positive value of the to find the first solution.
Step 7.3.2
Move all terms not containing to the right side of the equation.
Step 7.3.2.1
Add to both sides of the equation.
Step 7.3.2.2