Solving Quadratic Equations by Completing the Square.

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Solving Quadratic Equations by Completing the Square

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Presentation transcript:

Solving Quadratic Equations by Completing the Square

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

How to Create a Perfect Square Trinomial l In the following perfect square trinomial, the third term is missing. x x + ____ l Find the third term by dividing the middle coefficient by 2 and then squaring it. l (14/2) = (7) 2 = ??? x x + 49

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

Solving Quadratic Equations by Completing the Square Step 1: Make sure the x 2 and x term are on the left side of the equation; and the constant term is on the right side. Step 2: On the left side of the equation, find the 3 rd term to create a perfect square trinomial. Add that term to both sides. Step 3: Factor the perfect square trinomial on the left side of the equation. Simplify the right side of the equation. Step 4: Take the square root of each side Step 5: Set up the two equations and solve for x.

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

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.

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.

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

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

Completing the Square-Example #2 Solve the following equation by completing the square: Step 1: Move quadratic term, and linear term to left side of the equation, the constant to the right side of the equation.

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.

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.

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

Solving Quadratic Equations by Completing the Square

Solve the following equation by completing the square:

Solving Quadratic Equations by Completing the Square WARM-UP:

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