# Precalculus Examples

,
Step 1
Simplify .
Step 1.1
Apply the distributive property.
Step 1.2
Simplify the expression.
Step 1.2.1
Multiply by .
Step 1.2.2
Move to the left of .
Step 2
Subtract from both sides of the equation.
Step 3
Use the quadratic formula to find the solutions.
Step 4
Substitute the values , , and into the quadratic formula and solve for .
Step 5
Simplify.
Step 5.1
Simplify the numerator.
Step 5.1.1
Raise to the power of .
Step 5.1.2
Multiply .
Step 5.1.2.1
Multiply by .
Step 5.1.2.2
Multiply by .
Step 5.1.3
Step 5.1.4
Rewrite as .
Step 5.1.4.1
Factor out of .
Step 5.1.4.2
Rewrite as .
Step 5.1.5
Pull terms out from under the radical.
Step 5.2
Multiply by .
Step 5.3
Simplify .
Step 6
Simplify the expression to solve for the portion of the .
Step 6.1
Simplify the numerator.
Step 6.1.1
Raise to the power of .
Step 6.1.2
Multiply .
Step 6.1.2.1
Multiply by .
Step 6.1.2.2
Multiply by .
Step 6.1.3
Step 6.1.4
Rewrite as .
Step 6.1.4.1
Factor out of .
Step 6.1.4.2
Rewrite as .
Step 6.1.5
Pull terms out from under the radical.
Step 6.2
Multiply by .
Step 6.3
Simplify .
Step 6.4
Change the to .
Step 7
Simplify the expression to solve for the portion of the .
Step 7.1
Simplify the numerator.
Step 7.1.1
Raise to the power of .
Step 7.1.2
Multiply .
Step 7.1.2.1
Multiply by .
Step 7.1.2.2
Multiply by .
Step 7.1.3
Step 7.1.4
Rewrite as .
Step 7.1.4.1
Factor out of .
Step 7.1.4.2
Rewrite as .
Step 7.1.5
Pull terms out from under the radical.
Step 7.2
Multiply by .
Step 7.3
Simplify .
Step 7.4
Change the to .
Step 8
The final answer is the combination of both solutions.
Step 9
Find the values of that produce a value within the interval .
Step 9.1
The interval does not contain . It is not part of the final solution.
is not on the interval
Step 9.2
The interval contains .
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form: