Completing

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Completing the Square
SPI 3103.3.2 Solve quadratic equations and
systems, and determine
roots of a higher order polynomial.
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SPI 3103.3.2 Solve quadratic equations and
systems, and determine roots of a higher order
polynomial. Check for Understanding
3103.3.7 Solve quadratic equations by factoring,
graphing, completing the square, extracting
square roots and using the quadratic formula.
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Completing the square is one of the methods used
to solve quadratic equations.
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The general form of a quadratic equation is
ax2 bx c 0, a ? 0
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Step 1 Write the equation in the form ax2 bx
c
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Step 2 If a ? 1, divide each term of the
equation by a.
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Step 3 Complete the Square Take ½ of b, and
square the result. Add the result to both
sides of the equation.
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Step 4 Factor the left side of the equation as a
trinomial square combine like terms on the right.
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Step 5 Solve the equation by taking the square
root of both sides.
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Solve x2 8x 3 0 by completing the square.
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x2 8x 3 0
x2 8x 3
x2 8x 16 3 16
(x 4)2 19
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v(x 4)2 v19
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v(x 4)2 v19
x 4 v19
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v(x 4)2 v19
x 4 v19
x 4 v19