How do you solve -4x^2+4000x=04x2+4000x=0?

1 Answer
Mar 2, 2018

The solutions are x=0,1000x=0,1000.

Explanation:

Simplify the quadratic by dividing by -44, then factor out an xx term. Lastly, solve for xx in the expression that equals 00.

-4x^2+4000x=04x2+4000x=0

(-4x^2+4000x)/color(red)(-4)=0/color(red)(-4)4x2+4000x4=04

x^2-1000x=0x21000x=0

x(x-1000)=0x(x1000)=0

x=0,1000x=0,1000

The solutions are x=0x=0 and x=1000x=1000. You can verify this answer by seeing where the parabola y=-4x^2+4000x=0y=4x2+4000x=0 crosses the xx-axis. (It crosses at 00 and 10001000.)

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