Solving Quadratic Equations

Factoring

100

x² = 6x + 91

x = {-7, 13}

200

4x² - 20x + 25 = 0

x = {5/2}

300

3x² - 3x - 60 = 0

x = {-4, 5}

400

4x² + 31x = 3x

x = {-7, 0}

500

4x² - 21x - 18 = 0

x = {-3/4, 6}

Square Roots

100

-2x² + 146 = -34

x = {+- 3 square root 10}

200

1/2 x² - 8 = 0

x = {+- 4}

300

9x² - 18 = 7

x = {+- 5/3}

400

1/3 x² - 7 = 43

x = {+- 5 square root 6}

500

-2x² - 196 = 0

x = {+-7i square root 2}

Completing the Square

100

x² - 14x = -44

7 +- square root 5

200

3x² + 6x - 62 = 7

-1 +-2 square root 6

300

2x² + 8x + 134 = 0

-2 +- 3i square root 7

400

x² + 18x + 97 = 0

-9 +- 4i

500

x² + 12x + 3 = 7

-6 +- 2 square root 10

Quadratic Formula

100

x² + 12x = 7x + 1

-5 +- square root 29/2

200

-x² + 7x = 1

7 +- 3 square root 5/2

300

5x² = x - 2

1 +- i square root 39/10

400

2x² - 9x + 8 = 0

9 +- square root 17/4

500

5x² + 4x + 1 = 0

-2 +- i/5

Discriminant

100

-2x² - 196

-1568, 2 imaginary roots

200

2x² - 9x + 8 = 0

17; 2 real, irrational roots

300

4x² - 21x - 18 = 0

729; 2 real, rational roots

400

x² + 18x + 97 = 0

-64; 2 imaginary roots

500

4x² - 20x + 25 = 0

0; 1 real, rational root