Solving Quadratic Equations by Completing the Square - PowerPoint Presentation

Slide1

Solving Quadratic Equations by Completing the SquareSlide2

Perfect Square Trinomials

Examples

x

2

+ 6x + 9

x

2

- 10x + 25

x

2

+ 12x + 36Slide3

Creating a Perfect

Square Trinomial

X

2

+ 14x + ____ Find the constant term by squaring half of b(14/2)2 X2 + 14x + 49 Factored this becomes (x+7)2

14/2 – half of bSlide4

Perfect Square Trinomials

Create perfect square trinomials.

x

2

+ 20x + ___x2 - 4x + ___x2 + 5x + ___

100

4

25/4Slide5

To solve by completing the square

If a quadratic equation does not factor we can solve it by two different methods

1.) Completing the Square (today’s lesson)

2.) Quadratic Formula (tomorrow’s lesson)Slide6

Steps to solve by

completing

the square

1.) If the quadratic does not factor, move c to the other side of the equation, leave space on left!

x²-4x -7 =0 x²-4x =72.) Make the left side a perfect square trinomial and add number to both sides of equation x² -4x 4/2= 2²=4 x² -4x +4 = 7 +43.)Factor your trinomial square (x-2)² =114.)Solve by square roots method x-2 = ±√11 x = 2±√11Slide7

Example

Solve the following equation by

completing the square:

Step 1:

Move quadratic term, and linear term to left side of the equationSlide8

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.Slide9

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. Slide10

Solving Quadratic Equations by Completing the Square

Step 4:

Take the square root of each sideSlide11

Solving Quadratic Equations by Completing the Square

Step 5:

Set up the two possibilities and solveSlide12
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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.