# Precalculus Examples

,

Step 1

Subtract from both sides of the equation.

Step 2

Step 2.1

For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .

Step 2.1.1

Factor out of .

Step 2.1.2

Rewrite as plus

Step 2.1.3

Apply the distributive property.

Step 2.2

Factor out the greatest common factor from each group.

Step 2.2.1

Group the first two terms and the last two terms.

Step 2.2.2

Factor out the greatest common factor (GCF) from each group.

Step 2.3

Factor the polynomial by factoring out the greatest common factor, .

Step 3

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Step 4

Step 4.1

Set equal to .

Step 4.2

Add to both sides of the equation.

Step 5

Step 5.1

Set equal to .

Step 5.2

Solve for .

Step 5.2.1

Subtract from both sides of the equation.

Step 5.2.2

Divide each term in by and simplify.

Step 5.2.2.1

Divide each term in by .

Step 5.2.2.2

Simplify the left side.

Step 5.2.2.2.1

Cancel the common factor of .

Step 5.2.2.2.1.1

Cancel the common factor.

Step 5.2.2.2.1.2

Divide by .

Step 5.2.2.3

Simplify the right side.

Step 5.2.2.3.1

Move the negative in front of the fraction.

Step 6

The final solution is all the values that make true.

Step 7

Step 7.1

The interval does not contain . It is not part of the final solution.

is not on the interval

Step 7.2

The interval contains .