Solving Quadratic Equations

Factoring

100

Solve by Factoring: x² - x - 12 = 0

x = -3, 4

200

Solve by Factoring: x² + 4x = -3

x = -3, -1

300

Solve by Factoring: 4x² - 44x + 120 = 0

x = 5, 6

400

Solve by Factoring: 2x² - 9x - 5 = 0

x = -1/2, 5

500

Solve by Factoring: 2x² + 19x = -24

x = -8, -3/2

Square Root Method

100

Solve using the Square Root Method: 

4x²=9

x = -3/2, 3/2

200

Solve using the Square Root Method:

3x² - 75 = 0

x = -5, 5

300

Solve using the Square Root Method:

8x² + 72 = 0

x = -3i, 3i

400

Solve using the Square Root Method:

(x - 5)² = 9

x = 2, 8

500

Solve using the Square Root Method:

(x + 3)² = 20

x = -3 +/- 2sqrt(5) 

Completing the Square

100

Solve using Completing the Square:

x² + 12x = 0

x = -6

200

Solve using Completing the Square:

x² - 6x = -5

x = 1, 5

300

Solve using Completing the Square:

x² - 4x - 26 = 0

x = 2 +/- sqrt(30) 

400

Solve using Completing the Square:

x² + 6x = -16

x = -3 +/- i sqrt(7) 

500

Solve using Completing the Square:

3x² + 6x - 7 = 0

Hint: divide everything by 3 first!

x = -1 +/- sqrt(7/3) 

Quadratic Formula

100

Solve using the Quadratic Formula:

3x² - 5x - 2 = 0

x = -1/3, 2

200

Solve using the Quadratic Formula:

2x² - 3x = 5

x = -1, 5/2

300

Solve using Quadratic Formula:

6x² - 5x = 4

x = -1/2, 4/3

400

Solve using Quadratic Formula:

x² - 3x + 1 = 0

x = (3 +/- sqrt[5])/2

500

Solve using Quadratic Formula:

x² + 5x = -2

x = (-5 +/- sqrt[17])/2

Any Quadratic Method

100

Solve using Quadratic Methods:

p^2/3 - 2^1/3 - 8 = 0

p = -8, 64

200

Solve using Quadratic Methods:

y^2/3 - y^1/3 = 12

y = -27, 64

300

Solve using Quadratic Methods:

4x⁴ + 7x² - 2 = 0

x = +/- 1/2 and +/-i sqrt(2)

400

Solve using Quadratic Methods:

x - x^1/2 - 12 = 0

x = 16

500

Solve using Quadratic Methods:

(2x² - 5)² - 16(2x² - 5) + 39 = 0

HINT: u= (2x² - 5)

x = -3, 3, -2, 2