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

Mar 2, 2018

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 $0$.

$- 4 {x}^{2} + 4000 x = 0$

$\frac{- 4 {x}^{2} + 4000 x}{\textcolor{red}{- 4}} = \frac{0}{\textcolor{red}{- 4}}$

${x}^{2} - 1000 x = 0$

$x \left(x - 1000\right) = 0$

$x = 0 , 1000$

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

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