MODELING COMPLETING THE SQUARE

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MODELING COMPLETING THE SQUARE
Use algebra tiles to complete a perfect square
trinomial.
Model the expression x 2 6x.
Arrange the x-tiles to form part of a square.
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1
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To complete the square, add nine 1-tiles.
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x2 6x 9 (x 3)2
You have completed the square.
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To complete the square of the expression x2 bx,
add the square of half the coefficient of x.
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What term should you add to x2 8x so that the
result is a perfect square?
SOLUTION
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Factor 2x2 x 2 0
SOLUTION
2x2 x 2 0
Write original equation.
2x2 x 2
Add 2 to each side.
Divide each side by 2.
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Write left side as a fraction.
Find the square root of each side.
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You can check the solutions on a graphing
calculator.
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CHOOSING A SOLUTION METHOD
Investigating the Quadratic Formula
ax2 bx c
Subtract c from each side.
Divide each side by a.
Add the square of half the coefficient of x to
each side.
Write the left side as a perfect square.
Use a common denominator to express the right
side as a single fraction.
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CHOOSING A SOLUTION METHOD
Investigating the Quadratic Formula
Find the square root of each side.Include on
the right side.
Solve for x by subtracting the same term from
each side.
Use a common denominator to express the right
side as a single fraction.