Finite Math Examples

Solve for x 26x-169-x^2<0
Step 1
Convert the inequality to an equation.
Step 2
Factor the left side of the equation.
Tap for more steps...
Step 2.1
Factor out of .
Tap for more steps...
Step 2.1.1
Reorder the expression.
Tap for more steps...
Step 2.1.1.1
Move .
Step 2.1.1.2
Reorder and .
Step 2.1.2
Factor out of .
Step 2.1.3
Factor out of .
Step 2.1.4
Rewrite as .
Step 2.1.5
Factor out of .
Step 2.1.6
Factor out of .
Step 2.2
Factor using the perfect square rule.
Tap for more steps...
Step 2.2.1
Rewrite as .
Step 2.2.2
Check that the middle term is two times the product of the numbers being squared in the first term and third term.
Step 2.2.3
Rewrite the polynomial.
Step 2.2.4
Factor using the perfect square trinomial rule , where and .
Step 3
Divide each term in by and simplify.
Tap for more steps...
Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
Tap for more steps...
Step 3.2.1
Dividing two negative values results in a positive value.
Step 3.2.2
Divide by .
Step 3.3
Simplify the right side.
Tap for more steps...
Step 3.3.1
Divide by .
Step 4
Set the equal to .
Step 5
Add to both sides of the equation.
Step 6
Use each root to create test intervals.
Step 7
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Tap for more steps...
Step 7.1
Test a value on the interval to see if it makes the inequality true.
Tap for more steps...
Step 7.1.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 7.1.2
Replace with in the original inequality.
Step 7.1.3
The left side is less than the right side , which means that the given statement is always true.
True
True
Step 7.2
Test a value on the interval to see if it makes the inequality true.
Tap for more steps...
Step 7.2.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 7.2.2
Replace with in the original inequality.
Step 7.2.3
The left side is less than the right side , which means that the given statement is always true.
True
True
Step 7.3
Compare the intervals to determine which ones satisfy the original inequality.
True
True
True
True
Step 8
The solution consists of all of the true intervals.
or
Step 9
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 10