Question

When 30 times a number is increased by 32 ,the result is equal to twice the square of the number. Find the number

Answer 1

x = number

When 30 times a number is increased by 32 ,the result is equal to twice the square of the number means:

30 x + 32 = 2 x²

Subtract 2 x² to both sides

- 2 x² + 30 x + 32 = 0

Divide both sides by - 2

x² - 15 x - 16 = 0

The solutions are:

x = - 1

and

x = 16

Check of results:

30 x + 32 = 2 x²

30 ∙ ( - 1 ) + 32 = 2 ∙ ( - 1 )²

-30 + 32 = 2 ∙ 1

2 = 2

30 ∙ 16 + 32 = 2 ∙ 16²

480 + 32 = 2 ∙ 256

512 = 512

Answer 2

512

Answer 3

The number is 16.