Equations

Quadratic

100

2x² - 32 = 0

(x - 4) (x + 4)

200

x² + 5x + 6 = 0

x = -3      x = -2

300

2x² + 8x - 10 = 0

x = -5      x = 1

400

2x² - 6x - 7 = 0

x = 0.8979    x = 3.8979

500

3x² + x + 5x - 10 = -5x² + 2x² -4x -3x + 10 - 15

x = -5/2    x = 1/3

Simultaneous

100

6a + b = 18 

4a + b = 14 

x = 2

y = 6

200

2x + 4y = 14 

4x − 4y = 4 

x = 3

y = 2

300

10s + 4t = 108

10s + 25t = 360

s = 6

t = 12

400

3y +  2x = 6

5x + 2y = 15

x = 3

y = 0

500

x = -3

3x - 2y = 7

x = -3

y = -8

Rational

100

3/x + 1/4 = 8/x

x = 20

200

3/5x + x + 3/7x

x = 6/5 or 1 1/5 or 1.2

300

10x/3x + 5x/3 = 5

x = 1

400

x/5 = 3/x-2

x = -3

x = 5

500

2x/4x + 1/8 = 10/x

x = 36

Linear

100

6x + 8 = 14

x = 1

200

4x + 20 = 44 + 12x

x = -3

300

5x- 3x+ 6 = 20 - 10 + 3x

x = -4

400

10x - 5 = 2x - 12

x = -7/8 or x = -0.875

500

7x + 9 - 2x - 3 - 5x + 4 + 3x - 2

X = 4

Index & Forming and Solving

100

2^{n + 8} = 2⁵ⁿ

n = 2

200

3^{x - 5} + 9^{x + 1}

x = -7

300

64^{x - 8} = 256^{3x + 3}

x = -4

400

The length of a rectangle is 4 cm more than its width. If the area of the rectangle is 60 square centimeters, find the dimensions of the rectangle.

x = -10

x = 6

500

When 6 is subtracted from the square of a number, the result is 5 times the number. Find the positive solution.

x = 6