# Finite Math Examples

,
Step 1
Solve for in .
Step 1.1
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
Step 1.2.2.1
Dividing two negative values results in a positive value.
Step 1.2.2.2
Divide by .
Step 1.2.3
Simplify the right side.
Step 1.2.3.1
Simplify each term.
Step 1.2.3.1.1
Divide by .
Step 1.2.3.1.2
Dividing two negative values results in a positive value.
Step 1.2.3.1.3
Divide by .
Step 2
Replace all occurrences of with in each equation.
Step 2.1
Replace all occurrences of in with .
Step 2.2
Simplify the left side.
Step 2.2.1
Simplify each term.
Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
Multiply by .
Step 3
Solve for in .
Step 3.1
Add to both sides of the equation.
Step 3.2
Step 3.3
Factor the left side of the equation.
Step 3.3.1
Factor out of .
Step 3.3.1.1
Reorder and .
Step 3.3.1.2
Factor out of .
Step 3.3.1.3
Factor out of .
Step 3.3.1.4
Rewrite as .
Step 3.3.1.5
Factor out of .
Step 3.3.1.6
Factor out of .
Step 3.3.2
Factor.
Step 3.3.2.1
Factor using the AC method.
Step 3.3.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 3.3.2.1.2
Write the factored form using these integers.
Step 3.3.2.2
Remove unnecessary parentheses.
Step 3.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.5
Set equal to and solve for .
Step 3.5.1
Set equal to .
Step 3.5.2
Add to both sides of the equation.
Step 3.6
Set equal to and solve for .
Step 3.6.1
Set equal to .
Step 3.6.2
Subtract from both sides of the equation.
Step 3.7
The final solution is all the values that make true.
Step 4
Replace all occurrences of with in each equation.
Step 4.1
Replace all occurrences of in with .
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
Replace all occurrences of with in each equation.
Step 5.1
Replace all occurrences of in with .
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