Precalculus Examples

Solve by Completing the Square
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
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 .
Raise to the power of to get .
Add and to get .
Simplify each term.
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Remove parentheses around .
Raise to the power of to get .
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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Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Add and to get .
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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Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Subtract from to get .
The complete solution is the result of both the positive and negative portions of the solution.
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