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Solving Quadratic Equations by Completing the Square.

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Presentation on theme: "Solving Quadratic Equations by Completing the Square."— Presentation transcript:

1 Solving Quadratic Equations by Completing the Square

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

3 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

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

5 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

6 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.

7 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.

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

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

10 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.

11 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.

12 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.

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

14 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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