Finite Math Examples

Find the Roots (Zeros) (-x^2)/((1+4x)^2)=5/4
Step 1
Move the negative in front of the fraction.
Step 2
Find the LCD of the terms in the equation.
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Step 2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 2.2
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 2.3
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
Step 2.4
has factors of and .
Step 2.5
Multiply by .
Step 2.6
The factors for are , which is multiplied by itself times.
occurs times.
Step 2.7
The LCM of is the result of multiplying all factors the greatest number of times they occur in either term.
Step 2.8
The Least Common Multiple of some numbers is the smallest number that the numbers are factors of.
Step 3
Multiply each term in by to eliminate the fractions.
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Step 3.1
Multiply 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
Move the leading negative in into the numerator.
Step 3.2.1.2
Factor out of .
Step 3.2.1.3
Cancel the common factor.
Step 3.2.1.4
Rewrite the expression.
Step 3.2.2
Multiply by .
Step 3.3
Simplify the right side.
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Step 3.3.1
Cancel the common factor of .
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Step 3.3.1.1
Factor out of .
Step 3.3.1.2
Cancel the common factor.
Step 3.3.1.3
Rewrite the expression.
Step 4
Solve the equation.
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Step 4.1
Simplify .
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Step 4.1.1
Rewrite as .
Step 4.1.2
Expand using the FOIL Method.
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Step 4.1.2.1
Apply the distributive property.
Step 4.1.2.2
Apply the distributive property.
Step 4.1.2.3
Apply the distributive property.
Step 4.1.3
Simplify and combine like terms.
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Step 4.1.3.1
Simplify each term.
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Step 4.1.3.1.1
Multiply by .
Step 4.1.3.1.2
Multiply by .
Step 4.1.3.1.3
Multiply by .
Step 4.1.3.1.4
Rewrite using the commutative property of multiplication.
Step 4.1.3.1.5
Multiply by by adding the exponents.
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Step 4.1.3.1.5.1
Move .
Step 4.1.3.1.5.2
Multiply by .
Step 4.1.3.1.6
Multiply by .
Step 4.1.3.2
Add and .
Step 4.1.4
Apply the distributive property.
Step 4.1.5
Simplify.
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Step 4.1.5.1
Multiply by .
Step 4.1.5.2
Multiply by .
Step 4.1.5.3
Multiply by .
Step 4.2
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 4.3
Move all terms containing to the left side of the equation.
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Step 4.3.1
Add to both sides of the equation.
Step 4.3.2
Add and .
Step 4.4
Use the quadratic formula to find the solutions.
Step 4.5
Substitute the values , , and into the quadratic formula and solve for .
Step 4.6
Simplify.
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Step 4.6.1
Simplify the numerator.
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Step 4.6.1.1
Raise to the power of .
Step 4.6.1.2
Multiply .
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Step 4.6.1.2.1
Multiply by .
Step 4.6.1.2.2
Multiply by .
Step 4.6.1.3
Subtract from .
Step 4.6.1.4
Rewrite as .
Step 4.6.1.5
Rewrite as .
Step 4.6.1.6
Rewrite as .
Step 4.6.1.7
Rewrite as .
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Step 4.6.1.7.1
Factor out of .
Step 4.6.1.7.2
Rewrite as .
Step 4.6.1.8
Pull terms out from under the radical.
Step 4.6.1.9
Move to the left of .
Step 4.6.2
Multiply by .
Step 4.6.3
Simplify .
Step 4.7
The final answer is the combination of both solutions.
Step 5