Solving Quadratic Equations

Solving Quadratics

100

Solve the following quadratic equation (i.e. set = 0)

 (x - 7)(x + 2) = 0

x = 7 x = -2 

or x = { 7, -2}

200

Solve the following quadratic equation by factoring. x²+3x+2 = 0

x = -2 x = -1

300

Solve the following quadratic equation by factoring. x² - 6x + 5 = 0

x = 5 x = 1

400

Solve the following quadratic equation by factoring.

 x² - 6x - 27 = 0

x = 9 x = -3

500

Solve the following quadratic equation by factoring. 2x² - 5x - 3 = 0

x = -1/2 x = 3

Mixed

100

Factor the expression completely:

36x - 6

6(6x - 1)

200

Solve the equation:

16 - 10x = 0

2(8 - 5x) = 0

2 = 0

8 - 5x = 0

x = 8/5

300

Factor the expression completely:

1 - x²

(1 + x)(1 - x)

400

Solve by the following:

x² + 8x + 76 = -10x - 4

(x + 8)(x + 10) = 0

x = -8

x = -10

500

Solve the following by completing the square, express your answer in simplest radical form.

x² - 14x + 36 = 0

x = 7 + radical 13

x = 7 - radical 13

Factoring Quadratics

100

Factor:  9x - 21

3(3x - 7)

200

Factor:  16x² - 121

(4x - 11)(4x + 11)

300

Factor:  x² - 8x + 15

(x - 3)(x - 5)

400

Factor completely:  8 - 50x²

2(4 - 25x²) = 

2(2 - 5x)(2 + 5x)

500

Factor completely:  4x² + 8x - 60

4(x² + 2x - 15) = 

4(x - 3)(x + 5)

Quadratic Formula

100

What is the quadratic formula?

x=(-b +- sqrt(b^2-4ac))/(2a)

200

Identify a, b and c in the following equation: 

x² + 6x + 5 = 0

a = 1; b = 6; c = 5

300

Identify a, b and c in the following equation: 

x² - 9x + 20 = 9

a = 1; b = -9; c = 11

400

Solve the following quadratic equation by using the quadratic formula: 2x² + 9x + 4 = 0

-b +/- sqrt(b² - 4ac) /2a

-9 +/- sqrt(81 - 4(2)(4) /2(2)

-9 +/- sqrt(81 - 32) /4

-9 +/- sqrt 49/ 4

-9 +/- 7 /4 = -2/4 and -16/4         x = -1/2 x = -4

500

Solve the following quadratic equation by using the quadratic formula: 4x² - 17x - 15 = 0

x = -b +/- sqrt(b² - 4(4)(-15) /2a

x = 17 +/- sqrt(289 + 240) /8

x = 17 +/- sqrt (529) /8 = x = 17 +/- 23 /8

x = 40/8 x = -6/8  or

x = 5 x = -3/4

What's the best method?

100

What is the best method for factoring the following?

x²+6x+9 = 0

Trick Method

or

AM Method

200

What is the best method for factoring the following?

x²- 4 = 0

D2PS

300

What is the best method for factoring the following?

5x²+2x-2 = 0

Quadratic Formula

400

What is the best method for factoring the following?

x²-7x+5 = 0

Quadratic Formula

500

True or false?

Using the quadratic formula and factoring will give you different results.

False