Pre-Algebra Examples

Find the Quadratic Constant of Variation 5x^2y+8xy^2=-2
Step 1
Add to both sides of the equation.
Step 2
Use the quadratic formula to find the solutions.
Step 3
Substitute the values , , and into the quadratic formula and solve for .
Step 4
Simplify.
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Step 4.1
Simplify the numerator.
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Step 4.1.1
Apply the product rule to .
Step 4.1.2
Raise to the power of .
Step 4.1.3
Multiply the exponents in .
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Step 4.1.3.1
Apply the power rule and multiply exponents, .
Step 4.1.3.2
Multiply by .
Step 4.1.4
Multiply by .
Step 4.1.5
Multiply by .
Step 4.1.6
Factor out of .
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Step 4.1.6.1
Factor out of .
Step 4.1.6.2
Factor out of .
Step 4.1.6.3
Factor out of .
Step 4.2
Multiply by .
Step 5
Simplify the expression to solve for the portion of the .
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Step 5.1
Simplify the numerator.
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Step 5.1.1
Apply the product rule to .
Step 5.1.2
Raise to the power of .
Step 5.1.3
Multiply the exponents in .
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Step 5.1.3.1
Apply the power rule and multiply exponents, .
Step 5.1.3.2
Multiply by .
Step 5.1.4
Multiply by .
Step 5.1.5
Multiply by .
Step 5.1.6
Factor out of .
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Step 5.1.6.1
Factor out of .
Step 5.1.6.2
Factor out of .
Step 5.1.6.3
Factor out of .
Step 5.2
Multiply by .
Step 5.3
Change the to .
Step 5.4
Factor out of .
Step 5.5
Factor out of .
Step 5.6
Factor out of .
Step 5.7
Rewrite as .
Step 5.8
Move the negative in front of the fraction.
Step 6
Simplify the expression to solve for the portion of the .
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Step 6.1
Simplify the numerator.
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Step 6.1.1
Apply the product rule to .
Step 6.1.2
Raise to the power of .
Step 6.1.3
Multiply the exponents in .
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Step 6.1.3.1
Apply the power rule and multiply exponents, .
Step 6.1.3.2
Multiply by .
Step 6.1.4
Multiply by .
Step 6.1.5
Multiply by .
Step 6.1.6
Factor out of .
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Step 6.1.6.1
Factor out of .
Step 6.1.6.2
Factor out of .
Step 6.1.6.3
Factor out of .
Step 6.2
Multiply by .
Step 6.3
Change the to .
Step 6.4
Factor out of .
Step 6.5
Factor out of .
Step 6.6
Factor out of .
Step 6.7
Rewrite as .
Step 6.8
Move the negative in front of the fraction.
Step 7
The final answer is the combination of both solutions.
Step 8
The given equation can not be written as , so doesn't vary directly with .
doesn't vary directly with