Finite Math Examples

Solve by Completing the Square x^2-5x=5
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
Raise to the power of .
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
Raise to the power of .
Step 3.2.1.1.5
Raise to the power of .
Step 3.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.2.1.3
Combine and .
Step 3.2.1.4
Combine the numerators over the common denominator.
Step 3.2.1.5
Simplify the numerator.
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Step 3.2.1.5.1
Multiply by .
Step 3.2.1.5.2
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
Simplify the numerator.
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Step 5.2.2.1
Rewrite as .
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Step 5.2.2.1.1
Factor out of .
Step 5.2.2.1.2
Rewrite as .
Step 5.2.2.2
Pull terms out from under the radical.
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
Add to both sides of the equation.
Step 6
The result can be shown in multiple forms.
Exact Form:
Decimal Form: