Pre-Algebra Examples

Solve Using the Square Root Property 20x^5=125x
Step 1
Subtract from both sides of the equation.
Step 2
Factor the left side of the equation.
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Step 2.1
Factor out of .
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Step 2.1.1
Factor out of .
Step 2.1.2
Factor out of .
Step 2.1.3
Factor out of .
Step 2.2
Rewrite as .
Step 2.3
Rewrite as .
Step 2.4
Factor.
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Step 2.4.1
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Step 2.4.2
Remove unnecessary parentheses.
Step 3
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4
Set equal to .
Step 5
Set equal to and solve for .
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Step 5.1
Set equal to .
Step 5.2
Solve for .
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Step 5.2.1
Subtract from both sides of the equation.
Step 5.2.2
Divide each term in by and simplify.
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Step 5.2.2.1
Divide each term in by .
Step 5.2.2.2
Simplify the left side.
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Step 5.2.2.2.1
Cancel the common factor of .
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Step 5.2.2.2.1.1
Cancel the common factor.
Step 5.2.2.2.1.2
Divide by .
Step 5.2.2.3
Simplify the right side.
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Step 5.2.2.3.1
Move the negative in front of the fraction.
Step 5.2.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5.2.4
Simplify .
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Step 5.2.4.1
Rewrite as .
Step 5.2.4.2
Pull terms out from under the radical.
Step 5.2.4.3
Rewrite as .
Step 5.2.4.4
Multiply by .
Step 5.2.4.5
Combine and simplify the denominator.
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Step 5.2.4.5.1
Multiply by .
Step 5.2.4.5.2
Raise to the power of .
Step 5.2.4.5.3
Raise to the power of .
Step 5.2.4.5.4
Use the power rule to combine exponents.
Step 5.2.4.5.5
Add and .
Step 5.2.4.5.6
Rewrite as .
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Step 5.2.4.5.6.1
Use to rewrite as .
Step 5.2.4.5.6.2
Apply the power rule and multiply exponents, .
Step 5.2.4.5.6.3
Combine and .
Step 5.2.4.5.6.4
Cancel the common factor of .
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Step 5.2.4.5.6.4.1
Cancel the common factor.
Step 5.2.4.5.6.4.2
Rewrite the expression.
Step 5.2.4.5.6.5
Evaluate the exponent.
Step 5.2.4.6
Simplify the numerator.
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Step 5.2.4.6.1
Combine using the product rule for radicals.
Step 5.2.4.6.2
Multiply by .
Step 5.2.4.7
Combine and .
Step 5.2.5
The complete solution is the result of both the positive and negative portions of the solution.
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Step 5.2.5.1
First, use the positive value of the to find the first solution.
Step 5.2.5.2
Next, use the negative value of the to find the second solution.
Step 5.2.5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 6
Set equal to and solve for .
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Step 6.1
Set equal to .
Step 6.2
Solve for .
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Step 6.2.1
Add to both sides of the equation.
Step 6.2.2
Divide each term in by and simplify.
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Step 6.2.2.1
Divide each term in by .
Step 6.2.2.2
Simplify the left side.
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Step 6.2.2.2.1
Cancel the common factor of .
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Step 6.2.2.2.1.1
Cancel the common factor.
Step 6.2.2.2.1.2
Divide by .
Step 6.2.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 6.2.4
Simplify .
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Step 6.2.4.1
Rewrite as .
Step 6.2.4.2
Multiply by .
Step 6.2.4.3
Combine and simplify the denominator.
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Step 6.2.4.3.1
Multiply by .
Step 6.2.4.3.2
Raise to the power of .
Step 6.2.4.3.3
Raise to the power of .
Step 6.2.4.3.4
Use the power rule to combine exponents.
Step 6.2.4.3.5
Add and .
Step 6.2.4.3.6
Rewrite as .
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Step 6.2.4.3.6.1
Use to rewrite as .
Step 6.2.4.3.6.2
Apply the power rule and multiply exponents, .
Step 6.2.4.3.6.3
Combine and .
Step 6.2.4.3.6.4
Cancel the common factor of .
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Step 6.2.4.3.6.4.1
Cancel the common factor.
Step 6.2.4.3.6.4.2
Rewrite the expression.
Step 6.2.4.3.6.5
Evaluate the exponent.
Step 6.2.4.4
Simplify the numerator.
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Step 6.2.4.4.1
Combine using the product rule for radicals.
Step 6.2.4.4.2
Multiply by .
Step 6.2.5
The complete solution is the result of both the positive and negative portions of the solution.
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Step 6.2.5.1
First, use the positive value of the to find the first solution.
Step 6.2.5.2
Next, use the negative value of the to find the second solution.
Step 6.2.5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 7
The final solution is all the values that make true.