Question

Think of a number, double the number,

square the result, then subtract the original
number, the result is 33. What is the
number?

Answer 1

3

Explanation:

Set up an equation for the scenario

`(2x)^2 - (x) = 33`

Solve for x by factoring

`(2x)^2 - x - 33 = 0`

`4x^2 - x - 33 = 0`

`4x^2+11x-12x-33`

`(4x^2+11x)(-12x-33)`

`x(4x+11)-3(4x+11)`

`(4x+11)(x-3)`

`x-3=0`

`x=3`

plug back in

`(2(3))^2 - (3) = 33`

`(2(3))^2 = 36`

`(2(3)) = √(36)`

`2(3) = 6`

`6 = 6` ✔️