Question

How come there are no solutions to the equation, `sqrtx = - 10`?

Answer 1

There is no real number that makes a negative number when squared.

Explanation:

Any positive number multiplied by itself (squared) produces a positive answer.

e.g. `2*2 = 4`

Any negative number multiplied by itself (squared) produces a positive answer.

e.g. `-2*-2 = 4`

The square root of a number is the number that multiplies by itself to produce the product.

`sqrtx * sqrtx = x`

If `x` is negative, there is no real number that is its square root.

Answer 2

If you were to square both sides, you would get `x=100`.
However, if you were to square root both sides of `x=100`, you would get `sqrtx=10`, where `sqrtx!=-10`.