Finite Math Examples

Solve by Completing the Square x^2-x=0
Step 1
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of .
Step 2
Add the term to each side of the equation.
Step 3
Simplify the equation.
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Step 3.1
Simplify the left side.
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Step 3.1.1
Simplify each term.
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Step 3.1.1.1
Use the power rule to distribute the exponent.
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Step 3.1.1.1.1
Apply the product rule to .
Step 3.1.1.1.2
Apply the product rule to .
Step 3.1.1.2
Raise to the power of .
Step 3.1.1.3
Multiply by .
Step 3.1.1.4
One to any power is one.
Step 3.1.1.5
Raise to the power of .
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
Simplify each term.
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Step 3.2.1.1.1
Use the power rule to distribute the exponent.
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Step 3.2.1.1.1.1
Apply the product rule to .
Step 3.2.1.1.1.2
Apply the product rule to .
Step 3.2.1.1.2
Raise to the power of .
Step 3.2.1.1.3
Multiply by .
Step 3.2.1.1.4
One to any power is one.
Step 3.2.1.1.5
Raise to the power of .
Step 3.2.1.2
Add and .
Step 4
Factor the perfect trinomial square into .
Step 5
Solve the equation for .
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Step 5.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 5.2
Simplify .
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Step 5.2.1
Rewrite as .
Step 5.2.2
Any root of is .
Step 5.2.3
Simplify the denominator.
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Step 5.2.3.1
Rewrite as .
Step 5.2.3.2
Pull terms out from under the radical, assuming positive real numbers.
Step 5.3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 5.3.1
First, use the positive value of the to find the first solution.
Step 5.3.2
Move all terms not containing to the right side of the equation.
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Step 5.3.2.1
Add to both sides of the equation.
Step 5.3.2.2
Combine the numerators over the common denominator.
Step 5.3.2.3
Add and .
Step 5.3.2.4
Divide by .
Step 5.3.3
Next, use the negative value of the to find the second solution.
Step 5.3.4
Move all terms not containing to the right side of the equation.
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Step 5.3.4.1
Add to both sides of the equation.
Step 5.3.4.2
Combine the numerators over the common denominator.
Step 5.3.4.3
Add and .
Step 5.3.4.4
Divide by .
Step 5.3.5
The complete solution is the result of both the positive and negative portions of the solution.