Solving Quadratic Equations

Graphing

100

x² + 8x = 0

0, -8

200

x² - 3x - 18 = 0

-3, 6

300

x² - 6x + 4 = -8

No solution

400

5x² + 10x - 4 = -6

between -2 and -1, between -1 and 0

500

x² - 20 = 2 + x

between -5 and -4, between 5 and 6

Factoring

100

x² - 9x = 0

0, 9

200

x² - 5x - 24 = 0

8, -3

300

x² - 3x - 28 = 0

-4, 7

400

2x² - 24x = -72

6

500

-8x² + 46x - 30 = 0

5, 3/4

Square Root Property

100

4x² + 32 = 0

+/- 2i(square root (2))

200

2x² + 24 = 0

+/- 2i(square root(3))

300

3x² + 48 = 0

+/- 4i

400

2x² + 10 = 0

+/- i(square root (5))

500

8x² + 128 = 0

+/- 4i

Completing the Square

100

x² + 2x - 8 = 0

-4, 2

200

x² - 4x + 9 = 0

2 - i(square root (5)), 2 + i(square root(5))

300

2x² - 3x - 3 = 0

-0.69, 2.19

400

2x² + 6x - 12 = 0

-4.37, 1.37

500

x² + 8x + 10 = 0

-6.45, -1.55

Quadratic Formula

100

x² + 12x - 9 = 0

-6 +/- 3(square root(5))

200

x² + 8x + 5 = 0

-4 +/- (square root(11))

300

10x² - 3 = 13x

1.5, -0.2

400

22x = 12x² + 6

1.5, 1/3

500

x² + 3 = -6x + 8

-3 +/- (square root(14))