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Completing the Square
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Main Concept
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Completing the square is the name of a process used to convert quadratic polynomials in the general form to the vertex form:
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Steps:
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1. Factor the leading coefficient out of the first two terms
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2. Complete the square by adding and subtracting the "magic number"
(the square of half the coefficient of  )
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3. Move the constant  outside the parentheses. Remember to multiply it by a.
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4. Factor the perfect square and add the remaining terms.
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Numerical Example:
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1. Factor the leading coefficient out of the first two terms
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2. Complete the square by adding and subtracting the "magic number"
(the square of half the coefficient of x)
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3. Move the constant  outside the parentheses. Remember to multiply it by 3.
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4. Factor the perfect square and add the remaining terms.
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Click on "Next Step" to follow the steps of completing the square. Click on "New Quadratic" to start from a different polynomial. Observe that the magic number is the square of half the coefficient of x.
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