# Algebra Examples

Find the Zeros by Completing the Square
Step 1
Plug in for .
Step 2
Simplify the equation into a proper form to complete the square.
Step 2.1
Remove parentheses.
Step 2.2
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2.3
Subtract from both sides of the equation.
Step 3
Divide each term in by and simplify.
Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
Step 3.2.1
Simplify each term.
Step 3.2.1.1
Cancel the common factor of .
Step 3.2.1.1.1
Cancel the common factor.
Step 3.2.1.1.2
Divide by .
Step 3.2.1.2
Cancel the common factor of and .
Step 3.2.1.2.1
Factor out of .
Step 3.2.1.2.2
Cancel the common factors.
Step 3.2.1.2.2.1
Factor out of .
Step 3.2.1.2.2.2
Cancel the common factor.
Step 3.2.1.2.2.3
Rewrite the expression.
Step 3.2.1.2.2.4
Divide by .
Step 3.3
Simplify the right side.
Step 3.3.1
Move the negative in front of the fraction.
Step 4
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 5
Add the term to each side of the equation.
Step 6
Simplify the equation.
Step 6.1
Simplify the left side.
Step 6.1.1
Raise to the power of .
Step 6.2
Simplify the right side.
Step 6.2.1
Simplify .
Step 6.2.1.1
Raise to the power of .
Step 6.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 6.2.1.3
Combine and .
Step 6.2.1.4
Combine the numerators over the common denominator.
Step 6.2.1.5
Simplify the numerator.
Step 6.2.1.5.1
Multiply by .
Step 6.2.1.5.2
Step 7
Factor the perfect trinomial square into .
Step 8
Solve the equation for .
Step 8.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 8.2
Simplify .
Step 8.2.1
Rewrite as .
Step 8.2.2
Simplify the numerator.
Step 8.2.2.1
Rewrite as .
Step 8.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 8.2.3
Multiply by .
Step 8.2.4
Combine and simplify the denominator.
Step 8.2.4.1
Multiply by .
Step 8.2.4.2
Raise to the power of .
Step 8.2.4.3
Raise to the power of .
Step 8.2.4.4
Use the power rule to combine exponents.
Step 8.2.4.5
Step 8.2.4.6
Rewrite as .
Step 8.2.4.6.1
Use to rewrite as .
Step 8.2.4.6.2
Apply the power rule and multiply exponents, .
Step 8.2.4.6.3
Combine and .
Step 8.2.4.6.4
Cancel the common factor of .
Step 8.2.4.6.4.1
Cancel the common factor.
Step 8.2.4.6.4.2
Rewrite the expression.
Step 8.2.4.6.5
Evaluate the exponent.
Step 8.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 8.3.1
First, use the positive value of the to find the first solution.
Step 8.3.2
Add to both sides of the equation.
Step 8.3.3
Next, use the negative value of the to find the second solution.
Step 8.3.4
Add to both sides of the equation.
Step 8.3.5
The complete solution is the result of both the positive and negative portions of the solution.
Step 9
The result can be shown in multiple forms.
Exact Form:
Decimal Form: