# Completing the Square SPI 3103.3.2 Solve quadratic equations and systems, and determine roots of a higher order polynomial.

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Completing the Square SPI 3103.3.2 Solve quadratic equations and systems, and determine roots of a higher order polynomial.

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.

Completing the square is one of the methods used to solve quadratic equations.

The general form of a quadratic equation is ax 2 + bx + c = 0, a ≠ 0

Step 1 Write the equation in the form ax 2 + bx = –c

Step 2 If a ≠ 1, divide each term of the equation by a.

Step 3 Complete the Square – Take ½ of b, and square the result. – Add the result to both sides of the equation.

Step 4 Factor the left side of the equation as a trinomial square; combine like terms on the right.

Step 5 Solve the equation by taking the square root of both sides.

Solve x 2 + 8x – 3 = 0 by completing the square.

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

√(x + 4) 2 = √19

x + 4 = ± √19

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

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