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Solving Quadratic Equations by Completing the Square

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Perfect Square Trinomials l Examples l x 2 + 6x + 9 l x x + 25 l x x + 36

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Creating a Perfect Square Trinomial l In the following perfect square trinomial, the constant term is missing. X x + ____ l Find the constant term by squaring half the coefficient of the linear term. l (14/2) 2 X x + 49

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Perfect Square Trinomials l Create perfect square trinomials. l x x + ___ l x 2 - 4x + ___ l x 2 + 5x + ___ /4

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Solving Quadratic Equations by Completing the Square Solve the following equation by completing the square: Step 1: Only quadratic term and linear term on the left side of the equation

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Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides.

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Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

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Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

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Solving Quadratic Equations by Completing the Square Step 5: Set up the two possibilities and solve

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Completing the Square-Example #2 Solve the following equation by completing the square: Step 1: Only quadratic term and linear term on the left side of the equation. Constant term on the right side of the equation.

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Solving Quadratic Equations by Completing the Square Step 2: Find the term that completes the square on the left side of the equation. Add that term to both sides. The quadratic coefficient must be equal to 1 before you complete the square, so you must divide all terms by the quadratic coefficient first.

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Solving Quadratic Equations by Completing the Square Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation.

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Solving Quadratic Equations by Completing the Square Step 4: Take the square root of each side

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Solving Quadratic Equations by Completing the Square Try the following examples. Do your work on your paper and then check your answers.

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