Trigonometry Examples

Solve for x (x^4+5x^2-36)(2x^2+9x-5)=0
Step 1
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2
Set equal to and solve for .
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Step 2.1
Set equal to .
Step 2.2
Solve for .
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Step 2.2.1
Substitute into the equation. This will make the quadratic formula easy to use.
Step 2.2.2
Factor using the AC method.
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Step 2.2.2.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 2.2.2.2
Write the factored form using these integers.
Step 2.2.3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 2.2.4
Set equal to and solve for .
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Step 2.2.4.1
Set equal to .
Step 2.2.4.2
Add to both sides of the equation.
Step 2.2.5
Set equal to and solve for .
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Step 2.2.5.1
Set equal to .
Step 2.2.5.2
Subtract from both sides of the equation.
Step 2.2.6
The final solution is all the values that make true.
Step 2.2.7
Substitute the real value of back into the solved equation.
Step 2.2.8
Solve the first equation for .
Step 2.2.9
Solve the equation for .
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Step 2.2.9.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.2.9.2
Simplify .
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Step 2.2.9.2.1
Rewrite as .
Step 2.2.9.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2.9.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.2.9.3.1
First, use the positive value of the to find the first solution.
Step 2.2.9.3.2
Next, use the negative value of the to find the second solution.
Step 2.2.9.3.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 2.2.10
Solve the second equation for .
Step 2.2.11
Solve the equation for .
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Step 2.2.11.1
Remove parentheses.
Step 2.2.11.2
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.2.11.3
Simplify .
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Step 2.2.11.3.1
Rewrite as .
Step 2.2.11.3.2
Rewrite as .
Step 2.2.11.3.3
Rewrite as .
Step 2.2.11.3.4
Rewrite as .
Step 2.2.11.3.5
Pull terms out from under the radical, assuming positive real numbers.
Step 2.2.11.3.6
Move to the left of .
Step 2.2.11.4
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.2.11.4.1
First, use the positive value of the to find the first solution.
Step 2.2.11.4.2
Next, use the negative value of the to find the second solution.
Step 2.2.11.4.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 2.2.12
The solution to is .
Step 3
Set equal to and solve for .
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Step 3.1
Set equal to .
Step 3.2
Solve for .
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Step 3.2.1
Factor by grouping.
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Step 3.2.1.1
For a polynomial of the form , rewrite the middle term as a sum of two terms whose product is and whose sum is .
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Step 3.2.1.1.1
Factor out of .
Step 3.2.1.1.2
Rewrite as plus
Step 3.2.1.1.3
Apply the distributive property.
Step 3.2.1.2
Factor out the greatest common factor from each group.
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Step 3.2.1.2.1
Group the first two terms and the last two terms.
Step 3.2.1.2.2
Factor out the greatest common factor (GCF) from each group.
Step 3.2.1.3
Factor the polynomial by factoring out the greatest common factor, .
Step 3.2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.2.3
Set equal to and solve for .
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Step 3.2.3.1
Set equal to .
Step 3.2.3.2
Solve for .
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Step 3.2.3.2.1
Add to both sides of the equation.
Step 3.2.3.2.2
Divide each term in by and simplify.
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Step 3.2.3.2.2.1
Divide each term in by .
Step 3.2.3.2.2.2
Simplify the left side.
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Step 3.2.3.2.2.2.1
Cancel the common factor of .
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Step 3.2.3.2.2.2.1.1
Cancel the common factor.
Step 3.2.3.2.2.2.1.2
Divide by .
Step 3.2.4
Set equal to and solve for .
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Step 3.2.4.1
Set equal to .
Step 3.2.4.2
Subtract from both sides of the equation.
Step 3.2.5
The final solution is all the values that make true.
Step 4
The final solution is all the values that make true.