3x^2-12x-24=0

Answer 1

3x^2- 12x - 24 = 0

Solve the quadratic equation by completing the square:

Divide both sides by 3:
x^2 - 4x - 8 = 0
Add 8 to both sides:
x^2 - 4x = 8
Add 4 to both sides:
x^2 - 4x + 4 = 12
Factor the left hand side:
(x - 2)^2 = 12
Take the square root of both sides:
|x - 2| = 2 sqrt(3)
Eliminate the absolute value:
x - 2 = -2 sqrt(3) or x - 2 = 2 sqrt(3)
Add 2 to both sides:
x = 2 - 2 sqrt(3) or x - 2 = 2 sqrt(3)
Add 2 to both sides:
x = 2 - 2 sqrt(3) or x = 2 + 2 sqrt(3)

Answer 2

A wheel made 672 revolutions at 35 1/5 revolutions per minute. How many minutes did it rotates?