9 5 COMPLETING THE SQUARE Factoring A process

COMPLETE THE SQUARE: 2 ax Procedure: 1) Find the values of a and b.

COMPLETE THE SQUARE: Ex: What integer is needed to complete the square: 2 x

SOLUTION: Following the steps given 1) a = 1 and b = 5 3)

FINDING THE SOLUTION: Using the Zero-Product property (x+2. 5) = 0 X = -2.

COMPLETING THE SQUARE: ax 2 + bx = C Ex: What is the solutions

2 SOLUTION: x +6 X=216 1) a = 1 and b = 6 3)

YOU TRY IT: Ex: What are the solutions of: 2 r -4 r=30

2 SOLUTION: R -4 r=30 1) a = 1 and b = -4 3)

REAL-WORLD: You are planting A flower garden Consisting of 3 Square plots Surrounded by

SOLUTION: Adding an x to x +2 both sides of the picture we get:

SOLUTION: To complete the square 2 we now put it in the ax +bx

VIDEOS: SOLVING BY FACTORING Solving by factoring: http: //www. khanacademy. org/math/algebra/quadratics /factoring_quadratics/v/Example%201: %20 Solving%20

VIDEOS: SOLVING BY FACTORING Solving by factoring: http: //www. khanacademy. org/math/algebra/quadratics/f actoring_quadratics/v/Example%202: %20 Solving%20

CLASSWORK: Page 508 -509: Problems: 4, 7, 15, 21, 25, 36, 37.

Slides: 17

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9. 5: COMPLETING THE SQUARE: Factoring: A process used to break down any polynomial into simpler polynomials. Zero-Product Property: For any real numbers a and b, If ab = 0 Then a = 0 or b = 0.

COMPLETE THE SQUARE: 2 ax Procedure: 1) Find the values of a and b. + bx

GOAL:

COMPLETE THE SQUARE: Ex: What integer is needed to complete the square: 2 x +5 x+ ___?

SOLUTION: Following the steps given 1) a = 1 and b = 5 3) x 2+5 x+6. 25 (x+2. 5)

FINDING THE SOLUTION: Using the Zero-Product property (x+2. 5) = 0 X = -2. 5 The solutions are x = -2. 5 twice. If something happens twice we only touch the x-axis at that point.

COMPLETING THE SQUARE: ax 2 + bx = C Ex: What is the solutions of the equation: 2 x +6 X=216

2 SOLUTION: x +6 X=216 1) a = 1 and b = 6 3) x 2+6 x+9 (x+3)

YOU TRY IT: Ex: What are the solutions of: 2 r -4 r=30

2 SOLUTION: R -4 r=30 1) a = 1 and b = -4 3) x 2 -4 x+4 (x-2)

REAL-WORLD: You are planting A flower garden Consisting of 3 Square plots Surrounded by 1 ft border. The total area of the garden and the border is 100 tf 2. What is the side length x of each square plot?

SOLUTION: Adding an x to x +2 both sides of the picture we get: 3 x +2 A=bh A = (x +2)(3 x +2) 100 = (x +2)(3 x +2) 2 100 = 3 x + 8 x + 4 FOIL

SOLUTION: To complete the square 2 we now put it in the ax +bx = c form: 100 = 3 x 2 + 8 x + 4 3 x 2 + 8 x = 100 - 4 2 3 x + 8 x = 96 We always prefer a to be 1, so divide by 3:

SOLUTION: Continue

VIDEOS: SOLVING BY FACTORING Solving by factoring: http: //www. khanacademy. org/math/algebra/quadratics /factoring_quadratics/v/Example%201: %20 Solving%20 a %20 quadratic%20 equation%20 by%20 factoring

VIDEOS: SOLVING BY FACTORING Solving by factoring: http: //www. khanacademy. org/math/algebra/quadratics/f actoring_quadratics/v/Example%202: %20 Solving%20 a%20 quadratic%20 equation%20 by%20 factoring http: //www. khanacademy. org/math/trigonometry/polynomial_and_ratio nal/quad_formula_tutorial/v/solving-quadratic-equations-by-completingthe-square

CLASSWORK: Page 508 -509: Problems: 4, 7, 15, 21, 25, 36, 37.