Algebra Examples

Solve by Completing the Square 2y^2+14y=-19
Step 1
Divide each term in by and simplify.
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Step 1.1
Divide each term in by .
Step 1.2
Simplify the left side.
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Step 1.2.1
Simplify each term.
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Step 1.2.1.1
Cancel the common factor of .
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Step 1.2.1.1.1
Cancel the common factor.
Step 1.2.1.1.2
Divide by .
Step 1.2.1.2
Cancel the common factor of and .
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Step 1.2.1.2.1
Factor out of .
Step 1.2.1.2.2
Cancel the common factors.
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Step 1.2.1.2.2.1
Factor out of .
Step 1.2.1.2.2.2
Cancel the common factor.
Step 1.2.1.2.2.3
Rewrite the expression.
Step 1.2.1.2.2.4
Divide by .
Step 1.3
Simplify the right side.
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Step 1.3.1
Move the negative in front of the fraction.
Step 2
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 3
Add the term to each side of the equation.
Step 4
Simplify the equation.
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Step 4.1
Simplify the left side.
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Step 4.1.1
Simplify each term.
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Step 4.1.1.1
Apply the product rule to .
Step 4.1.1.2
Raise to the power of .
Step 4.1.1.3
Raise to the power of .
Step 4.2
Simplify the right side.
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Step 4.2.1
Simplify .
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Step 4.2.1.1
Simplify each term.
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Step 4.2.1.1.1
Apply the product rule to .
Step 4.2.1.1.2
Raise to the power of .
Step 4.2.1.1.3
Raise to the power of .
Step 4.2.1.2
To write as a fraction with a common denominator, multiply by .
Step 4.2.1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.2.1.3.1
Multiply by .
Step 4.2.1.3.2
Multiply by .
Step 4.2.1.4
Combine the numerators over the common denominator.
Step 4.2.1.5
Simplify the numerator.
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Step 4.2.1.5.1
Multiply by .
Step 4.2.1.5.2
Add and .
Step 5
Factor the perfect trinomial square into .
Step 6
Solve the equation for .
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Step 6.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 6.2
Simplify .
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Step 6.2.1
Rewrite as .
Step 6.2.2
Simplify the denominator.
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Step 6.2.2.1
Rewrite as .
Step 6.2.2.2
Pull terms out from under the radical, assuming positive real numbers.
Step 6.3
Subtract from both sides of the equation.
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form: