Finite Math Examples

Solve for R 0=-14000/(1+R)+9000/((1+R)^2)+10000/((1+R)^3)
Step 1
Rewrite the equation as .
Step 2
Move the negative in front of the fraction.
Step 3
Find the LCD of the terms in the equation.
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Step 3.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.2
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Step 3.3
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 3.4
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Step 3.5
The factor for is itself.
occurs time.
Step 3.6
The factors for are , which is multiplied by itself times.
occurs times.
Step 3.7
The factors for are , which is multiplied by itself times.
occurs times.
Step 3.8
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 4
Multiply each term in by to eliminate the fractions.
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Step 4.1
Multiply each term in by .
Step 4.2
Simplify the left side.
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Step 4.2.1
Simplify each term.
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Step 4.2.1.1
Cancel the common factor of .
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Step 4.2.1.1.1
Move the leading negative in into the numerator.
Step 4.2.1.1.2
Factor out of .
Step 4.2.1.1.3
Cancel the common factor.
Step 4.2.1.1.4
Rewrite the expression.
Step 4.2.1.2
Cancel the common factor of .
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Step 4.2.1.2.1
Factor out of .
Step 4.2.1.2.2
Cancel the common factor.
Step 4.2.1.2.3
Rewrite the expression.
Step 4.2.1.3
Apply the distributive property.
Step 4.2.1.4
Multiply by .
Step 4.2.1.5
Cancel the common factor of .
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Step 4.2.1.5.1
Cancel the common factor.
Step 4.2.1.5.2
Rewrite the expression.
Step 4.2.2
Add and .
Step 4.3
Simplify the right side.
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Step 4.3.1
Multiply by .
Step 5
Solve the equation.
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Step 5.1
Factor the left side of the equation.
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Step 5.1.1
Factor out of .
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Step 5.1.1.1
Reorder and .
Step 5.1.1.2
Factor out of .
Step 5.1.1.3
Factor out of .
Step 5.1.1.4
Factor out of .
Step 5.1.1.5
Factor out of .
Step 5.1.1.6
Factor out of .
Step 5.1.2
Rewrite as .
Step 5.1.3
Expand using the FOIL Method.
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Step 5.1.3.1
Apply the distributive property.
Step 5.1.3.2
Apply the distributive property.
Step 5.1.3.3
Apply the distributive property.
Step 5.1.4
Simplify and combine like terms.
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Step 5.1.4.1
Simplify each term.
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Step 5.1.4.1.1
Multiply by .
Step 5.1.4.1.2
Multiply by .
Step 5.1.4.1.3
Multiply by .
Step 5.1.4.1.4
Multiply by .
Step 5.1.4.2
Add and .
Step 5.1.5
Apply the distributive property.
Step 5.1.6
Simplify.
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Step 5.1.6.1
Multiply by .
Step 5.1.6.2
Multiply by .
Step 5.1.7
Subtract from .
Step 5.1.8
Subtract from .
Step 5.2
Divide each term in by and simplify.
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Step 5.2.1
Divide each term in by .
Step 5.2.2
Simplify the left side.
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Step 5.2.2.1
Cancel the common factor of .
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Step 5.2.2.1.1
Cancel the common factor.
Step 5.2.2.1.2
Divide by .
Step 5.2.3
Simplify the right side.
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Step 5.2.3.1
Divide by .
Step 5.3
Use the quadratic formula to find the solutions.
Step 5.4
Substitute the values , , and into the quadratic formula and solve for .
Step 5.5
Simplify.
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Step 5.5.1
Simplify the numerator.
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Step 5.5.1.1
Raise to the power of .
Step 5.5.1.2
Multiply .
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Step 5.5.1.2.1
Multiply by .
Step 5.5.1.2.2
Multiply by .
Step 5.5.1.3
Add and .
Step 5.5.2
Multiply by .
Step 5.6
The final answer is the combination of both solutions.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: