Trigonometry Examples

Solve for x x^5-x^3=0
Step 1
Factor the left side of the equation.
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Step 1.1
Factor out of .
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Step 1.1.1
Factor out of .
Step 1.1.2
Factor out of .
Step 1.1.3
Factor out of .
Step 1.2
Rewrite as .
Step 1.3
Factor.
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Step 1.3.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 1.3.2
Remove unnecessary parentheses.
Step 2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
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
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.2.2
Simplify .
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Step 3.2.2.1
Rewrite as .
Step 3.2.2.2
Pull terms out from under the radical, assuming real numbers.
Step 4
Set equal to and solve for .
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Step 4.1
Set equal to .
Step 4.2
Subtract from both sides of the equation.
Step 5
Set equal to and solve for .
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Step 5.1
Set equal to .
Step 5.2
Add to both sides of the equation.
Step 6
The final solution is all the values that make true.