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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 ax 2 + bx + c = 0, a ≠ 0

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Step 1 Write the equation in the form ax 2 + 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 x 2 + 8x – 3 = 0 by completing the square.

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x 2 + 8x – 3 = 0 x 2 + 8x = 3 x 2 + 8x + 16 = 3 + 16 (x + 4) 2 = 19

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√(x + 4) 2 = √19

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x + 4 = ± √19

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√(x + 4) 2 = √19 x + 4 = ±√19 x = –4 ± √19

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