Pre-Algebra Examples

Find the Quadratic Constant of Variation x=3y^2-9
Step 1
Rewrite the equation as .
Step 2
Add to both sides of the equation.
Step 3
Divide each term in by and simplify.
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Step 3.1
Divide each term in by .
Step 3.2
Simplify the left side.
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Step 3.2.1
Cancel the common factor of .
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Step 3.2.1.1
Cancel the common factor.
Step 3.2.1.2
Divide by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Divide by .
Step 4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5
The complete solution is the result of both the positive and negative portions of the solution.
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Step 5.1
First, use the positive value of the to find the first solution.
Step 5.2
Next, use the negative value of the to find the second solution.
Step 5.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 6
To write as a fraction with a common denominator, multiply by .
Step 7
Combine and .
Step 8
Combine the numerators over the common denominator.
Step 9
Multiply by .
Step 10
Rewrite as .
Step 11
Multiply by .
Step 12
Combine and simplify the denominator.
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Step 12.1
Multiply by .
Step 12.2
Raise to the power of .
Step 12.3
Raise to the power of .
Step 12.4
Use the power rule to combine exponents.
Step 12.5
Add and .
Step 12.6
Rewrite as .
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Step 12.6.1
Use to rewrite as .
Step 12.6.2
Apply the power rule and multiply exponents, .
Step 12.6.3
Combine and .
Step 12.6.4
Cancel the common factor of .
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Step 12.6.4.1
Cancel the common factor.
Step 12.6.4.2
Rewrite the expression.
Step 12.6.5
Evaluate the exponent.
Step 13
Combine using the product rule for radicals.
Step 14
To write as a fraction with a common denominator, multiply by .
Step 15
Combine and .
Step 16
Combine the numerators over the common denominator.
Step 17
Multiply by .
Step 18
Rewrite as .
Step 19
Multiply by .
Step 20
Combine and simplify the denominator.
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Step 20.1
Multiply by .
Step 20.2
Raise to the power of .
Step 20.3
Raise to the power of .
Step 20.4
Use the power rule to combine exponents.
Step 20.5
Add and .
Step 20.6
Rewrite as .
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Step 20.6.1
Use to rewrite as .
Step 20.6.2
Apply the power rule and multiply exponents, .
Step 20.6.3
Combine and .
Step 20.6.4
Cancel the common factor of .
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Step 20.6.4.1
Cancel the common factor.
Step 20.6.4.2
Rewrite the expression.
Step 20.6.5
Evaluate the exponent.
Step 21
Combine using the product rule for radicals.
Step 22
Reorder factors in .
Step 23
The given equation can not be written as , so doesn't vary directly with .
doesn't vary directly with