Question

How do you solve `-4x^2+4000x=0`?

Answer 1

The solutions are `x=0,1000`.

Explanation:

Simplify the quadratic by dividing by `-4`, then factor out an `x` term. Lastly, solve for `x` in the expression that equals `0`.

`-4x^2+4000x=0`

`(-4x^2+4000x)/color(red)(-4)=0/color(red)(-4)`

`x^2-1000x=0`

`x(x-1000)=0`

`x=0,1000`

The solutions are `x=0` and `x=1000`. You can verify this answer by seeing where the parabola `y=-4x^2+4000x=0` crosses the `x`-axis. (It crosses at `0` and `1000`.)

graph{-4x^2+4000x [-1000, 2000, -1000000, 1500000]}