Calculus Examples

Solve for x 2x-250/(x^2)=0
Step 1
Find the LCD of the terms in the equation.
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Step 1.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 1.2
The LCM of one and any expression is the expression.
Step 2
Multiply each term in by to eliminate the fractions.
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Step 2.1
Multiply each term in by .
Step 2.2
Simplify the left side.
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Step 2.2.1
Simplify each term.
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Step 2.2.1.1
Multiply by by adding the exponents.
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Step 2.2.1.1.1
Move .
Step 2.2.1.1.2
Multiply by .
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Step 2.2.1.1.2.1
Raise to the power of .
Step 2.2.1.1.2.2
Use the power rule to combine exponents.
Step 2.2.1.1.3
Add and .
Step 2.2.1.2
Cancel the common factor of .
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Step 2.2.1.2.1
Move the leading negative in into the numerator.
Step 2.2.1.2.2
Cancel the common factor.
Step 2.2.1.2.3
Rewrite the expression.
Step 2.3
Simplify the right side.
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Step 2.3.1
Multiply by .
Step 3
Solve the equation.
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Step 3.1
Add to both sides of the equation.
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Factor the left side of the equation.
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Step 3.3.1
Factor out of .
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Step 3.3.1.1
Factor out of .
Step 3.3.1.2
Factor out of .
Step 3.3.1.3
Factor out of .
Step 3.3.2
Rewrite as .
Step 3.3.3
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Step 3.3.4
Factor.
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Step 3.3.4.1
Simplify.
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Step 3.3.4.1.1
Move to the left of .
Step 3.3.4.1.2
Raise to the power of .
Step 3.3.4.2
Remove unnecessary parentheses.
Step 3.4
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 3.5
Set equal to and solve for .
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Step 3.5.1
Set equal to .
Step 3.5.2
Add to both sides of the equation.
Step 3.6
Set equal to and solve for .
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Step 3.6.1
Set equal to .
Step 3.6.2
Solve for .
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Step 3.6.2.1
Use the quadratic formula to find the solutions.
Step 3.6.2.2
Substitute the values , , and into the quadratic formula and solve for .
Step 3.6.2.3
Simplify.
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Step 3.6.2.3.1
Simplify the numerator.
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Step 3.6.2.3.1.1
Raise to the power of .
Step 3.6.2.3.1.2
Multiply .
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Step 3.6.2.3.1.2.1
Multiply by .
Step 3.6.2.3.1.2.2
Multiply by .
Step 3.6.2.3.1.3
Subtract from .
Step 3.6.2.3.1.4
Rewrite as .
Step 3.6.2.3.1.5
Rewrite as .
Step 3.6.2.3.1.6
Rewrite as .
Step 3.6.2.3.1.7
Rewrite as .
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Step 3.6.2.3.1.7.1
Factor out of .
Step 3.6.2.3.1.7.2
Rewrite as .
Step 3.6.2.3.1.8
Pull terms out from under the radical.
Step 3.6.2.3.1.9
Move to the left of .
Step 3.6.2.3.2
Multiply by .
Step 3.6.2.4
The final answer is the combination of both solutions.
Step 3.7
The final solution is all the values that make true.