Solving Quadratic Equations

Quadratic Formula

100

x² + 2x - 3

What is {1, -3}

200

5r² = 80

What is {4, -4}

300

2k² + 9k = -7

What is {-1 , -7/2}

400

k² -31 - 2k = -6 - 3k² - 2k

What is {5/2, -5/2}

500

9n² = 4 + 7n

What is {7 + or - sqrt 193/18}

Factoring

100

(d + 1)(d - 8) = 0

What is {-1, 8}

200

7r² - 14r = -7

What is {1}

300

3r² - 16r - 7 = 5

What is {-2/3, 6}

400

-4k²  - 8k - 3 = -3 - 5k²

What is {8,0}

500

15a² - 3a = 3 - 7a 

What is {1/3, -3/5}

Square Root

100

n² - 5 = -4

What is {1, -1}

200

8b² - 7 = 193

What is {5, -5}

300

8n² - 6 = 306

{6.244, - 6.244}

400

5n² - 7 = 488

What is {9.949, -9.949}

500

3 - 4x² = -85

What is {4.69, - 4.69}

Completing the Square

100

x² + 14x - 15 = 0

What is {1, -15}

200

5k² = 60 - 20k

What is {2, -6}

300

n² = 18n + 40

What is {20 , -2}

400

3x² = -4 + 8x

What is {2 , 2/3}

500

r² - 4r - 91 = 7

What is {2 + sqrt 102, 2 - sqrt 102}

Mystery

100

Solve 4n - 2n = 4

What is n = 2

200

The sum of x and 2 divided by 4 is 8. 

What is x= 30

300

6(6v + 6) − 5 = 1 + 6v

What is {-1}

400

12(2k + 11) = 12(2k + 12)

What is {no solution}

500

Solve the system of equation:

−5x + y = −3 

3x − 8y = 24

What is {0 , -3}