# Algebra Examples

Find the Intersection
,
Step 1
Substitute for .
Step 2
Solve for .
Step 2.1
Subtract from both sides of the equation.
Step 2.2
Add to both sides of the equation.
Step 2.3
Factor the left side of the equation.
Step 2.3.1
Factor out of .
Step 2.3.1.1
Factor out of .
Step 2.3.1.2
Factor out of .
Step 2.3.1.3
Rewrite as .
Step 2.3.1.4
Factor out of .
Step 2.3.1.5
Factor out of .
Step 2.3.2
Factor.
Step 2.3.2.1
Factor using the AC method.
Step 2.3.2.1.1
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 2.3.2.1.2
Write the factored form using these integers.
Step 2.3.2.2
Remove unnecessary parentheses.
Step 2.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.5
Set equal to and solve for .
Step 2.5.1
Set equal to .
Step 2.5.2
Add to both sides of the equation.
Step 2.6
Set equal to and solve for .
Step 2.6.1
Set equal to .
Step 2.6.2
Subtract from both sides of the equation.
Step 2.7
The final solution is all the values that make true.