# How do you solve -sqrtx = -25x?

Aug 5, 2015

$x = 0$ and $x = \frac{1}{625}$

#### Explanation:

First, rewrite your equation by cancelling the minus sign

$\sqrt{x} = 25 x$

Right from the start, it's obvious that any solution you find must be positive, $x \ge 0$, since the square root of a negative number does not have a real number as a solution.

So, square both sides of the equation to get

${\left(\sqrt{x}\right)}^{2} = {\left(25 x\right)}^{2}$

$x = 625 {x}^{2}$

Move everything to one side of the equation and factor the resulting expression

$625 {x}^{2} - x = 0$

$x \left(625 x - 1\right) = 0$

This equation is equal to zero when wither $x = 0$ or when $\left(625 x - 1\right) = 0$, which is equivalent to having

$625 x - 1 = 0 \implies x = \frac{1}{625}$

Both solutions are valid because they satisfy the condition $x \ge 0$.