Question

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

Answer 1

`x = 0` and `x= 1/625`

Explanation:

First, rewrite your equation by cancelling the minus sign

`sqrt(x) = 25x`

Right from the start, it's obvious that any solution you find must be positive, `x>=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

`(sqrt(x))^2 = (25x)^2`

`x = 625x^2`

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

`625x^2 - x = 0`

`x(625x - 1) = 0`

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

`625x-1 = 0 => x= 1/625`

Both solutions are valid because they satisfy the condition `x>=0`.