# Calculus 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
Subtract from both sides of the equation.
Step 2.3
Subtract from .
Step 2.4
Factor the left side of the equation.
Step 2.4.1
Factor out of .
Step 2.4.1.1
Reorder and .
Step 2.4.1.2
Factor out of .
Step 2.4.1.3
Factor out of .
Step 2.4.1.4
Rewrite as .
Step 2.4.1.5
Factor out of .
Step 2.4.1.6
Factor out of .
Step 2.4.2
Factor using the perfect square rule.
Step 2.4.2.1
Rewrite as .
Step 2.4.2.2
Rewrite as .
Step 2.4.2.3
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 2.4.2.4
Rewrite the polynomial.
Step 2.4.2.5
Factor using the perfect square trinomial rule , where and .
Step 2.5
Divide each term in by and simplify.
Step 2.5.1
Divide each term in by .
Step 2.5.2
Simplify the left side.
Step 2.5.2.1
Dividing two negative values results in a positive value.
Step 2.5.2.2
Divide by .
Step 2.5.3
Simplify the right side.
Step 2.5.3.1
Divide by .
Step 2.6
Set the equal to .
Step 2.7
Solve for .
Step 2.7.1
Add to both sides of the equation.
Step 2.7.2
Divide each term in by and simplify.
Step 2.7.2.1
Divide each term in by .
Step 2.7.2.2
Simplify the left side.
Step 2.7.2.2.1
Cancel the common factor of .
Step 2.7.2.2.1.1
Cancel the common factor.
Step 2.7.2.2.1.2
Divide by .