Precalculus Examples

Solve by Completing the Square
Add to both sides of the equation.
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of , the coefficient of .
Add the term to each side of the equation.
Simplify the equation.
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Simplify the right side.
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Simplify each term.
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Remove parentheses around .
One to any power is one.
Add and .
Simplify each term.
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Remove parentheses around .
One to any power is one.
Factor the perfect trinomial square into .
Solve the equation for .
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Take the square root of each side of the equation to set up the solution for
Remove the perfect root factor under the radical to solve for .
Simplify the right side of the equation.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
The complete solution is the result of both the positive and negative portions of the solution.
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First, use the positive value of the to find the first solution.
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Add and .
Next, use the negative value of the to find the second solution.
Move all terms not containing to the right side of the equation.
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Subtract from both sides of the equation.
Subtract from .
The complete solution is the result of both the positive and negative portions of the solution.
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