Basic Math Examples

Solve for v 100000=1/2*((2850)v^2)
Step 1
Rewrite the equation as .
Step 2
Multiply both sides of the equation by .
Step 3
Simplify both sides of the equation.
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Step 3.1
Simplify the left side.
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Step 3.1.1
Simplify .
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Step 3.1.1.1
Combine and .
Step 3.1.1.2
Divide by .
Step 3.1.1.3
Cancel the common factor of .
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Step 3.1.1.3.1
Factor out of .
Step 3.1.1.3.2
Cancel the common factor.
Step 3.1.1.3.3
Rewrite the expression.
Step 3.1.1.4
Combine and .
Step 3.1.1.5
Combine and .
Step 3.1.1.6
Cancel the common factor of .
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Step 3.1.1.6.1
Cancel the common factor.
Step 3.1.1.6.2
Divide by .
Step 3.2
Simplify the right side.
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Step 3.2.1
Simplify .
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Step 3.2.1.1
Combine and .
Step 3.2.1.2
Divide by .
Step 3.2.1.3
Cancel the common factor of .
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Step 3.2.1.3.1
Factor out of .
Step 3.2.1.3.2
Factor out of .
Step 3.2.1.3.3
Cancel the common factor.
Step 3.2.1.3.4
Rewrite the expression.
Step 3.2.1.4
Combine and .
Step 4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5
Simplify .
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Step 5.1
Rewrite as .
Step 5.2
Simplify the numerator.
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Step 5.2.1
Rewrite as .
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Step 5.2.1.1
Factor out of .
Step 5.2.1.2
Rewrite as .
Step 5.2.2
Pull terms out from under the radical.
Step 5.3
Multiply by .
Step 5.4
Combine and simplify the denominator.
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Step 5.4.1
Multiply by .
Step 5.4.2
Raise to the power of .
Step 5.4.3
Raise to the power of .
Step 5.4.4
Use the power rule to combine exponents.
Step 5.4.5
Add and .
Step 5.4.6
Rewrite as .
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Step 5.4.6.1
Use to rewrite as .
Step 5.4.6.2
Apply the power rule and multiply exponents, .
Step 5.4.6.3
Combine and .
Step 5.4.6.4
Cancel the common factor of .
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Step 5.4.6.4.1
Cancel the common factor.
Step 5.4.6.4.2
Rewrite the expression.
Step 5.4.6.5
Evaluate the exponent.
Step 5.5
Simplify the numerator.
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Step 5.5.1
Combine using the product rule for radicals.
Step 5.5.2
Multiply by .
Step 6
The complete solution is the result of both the positive and negative portions of the solution.
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Step 6.1
First, use the positive value of the to find the first solution.
Step 6.2
Next, use the negative value of the to find the second solution.
Step 6.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form: