Trigonometry Examples

Solve for x 400000<-2p^2+6000p
Step 1
Rewrite so is on the left side of the inequality.
Step 2
Convert the inequality to an equation.
Step 3
Subtract from both sides of the equation.
Step 4
Factor out of .
Tap for more steps...
Step 4.1
Factor out of .
Step 4.2
Factor out of .
Step 4.3
Factor out of .
Step 4.4
Factor out of .
Step 5
Divide each term in by and simplify.
Tap for more steps...
Step 5.1
Divide each term in by .
Step 5.2
Simplify the left side.
Tap for more steps...
Step 5.2.1
Cancel the common factor of .
Tap for more steps...
Step 5.2.1.1
Cancel the common factor.
Step 5.2.1.2
Divide by .
Step 5.3
Simplify the right side.
Tap for more steps...
Step 5.3.1
Divide by .
Step 6
Use the quadratic formula to find the solutions.
Step 7
Substitute the values , , and into the quadratic formula and solve for .
Step 8
Simplify.
Tap for more steps...
Step 8.1
Simplify the numerator.
Tap for more steps...
Step 8.1.1
Raise to the power of .
Step 8.1.2
Multiply .
Tap for more steps...
Step 8.1.2.1
Multiply by .
Step 8.1.2.2
Multiply by .
Step 8.1.3
Subtract from .
Step 8.1.4
Rewrite as .
Tap for more steps...
Step 8.1.4.1
Factor out of .
Step 8.1.4.2
Rewrite as .
Step 8.1.5
Pull terms out from under the radical.
Step 8.2
Multiply by .
Step 8.3
Simplify .
Step 9
The final answer is the combination of both solutions.
Step 10
Use each root to create test intervals.
Step 11
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 11.1
Test a value on the interval to see if it makes the inequality true.
Tap for more steps...
Step 11.1.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 11.1.2
Replace with in the original inequality.
Step 11.1.3
The left side is not less than the right side , which means that the given statement is false.
False
False
Step 11.2
Test a value on the interval to see if it makes the inequality true.
Tap for more steps...
Step 11.2.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 11.2.2
Replace with in the original inequality.
Step 11.2.3
The left side is less than the right side , which means that the given statement is always true.
True
True
Step 11.3
Test a value on the interval to see if it makes the inequality true.
Tap for more steps...
Step 11.3.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 11.3.2
Replace with in the original inequality.
Step 11.3.3
The left side is not less than the right side , which means that the given statement is false.
False
False
Step 11.4
Compare the intervals to determine which ones satisfy the original inequality.
False
True
False
False
True
False
Step 12
The solution consists of all of the true intervals.
Step 13
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 14