Subtract from both sides of the inequality.

Convert the inequality to an equation.

Factor using the perfect square rule.

Rearrange terms.

Rewrite as .

Check the middle term by multiplying and compare this result with the middle term in the original expression.

Simplify.

Factor using the perfect square trinomial rule , where and .

Set the equal to .

Add to both sides of the equation.

Use each root to create test intervals.

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

True

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is greater than the right side , which means that the given statement is always true.

True

True

Compare the intervals to determine which ones satisfy the original inequality.

True

True

True

True

The solution consists of all of the true intervals.

or

or

Use the inequality to build the set notation.

Convert to Set Notation x^2+36>12x