Equation x2 = x0
For the equation x2 = x0 there are two solutions, that is x = 1 and x = –1. In the graph you can see that x = 0 is not an intersection point.
Explanation
You can see the two intersections in the graph.
This is one of the many explanations why 00 ≝ 1 is by definition so determined.
Algebraic solution
A calculation gives
x2 = x0 = 1
x2 − 1 = 0
(x − 1)(x + 1) = 0 ⇒ x1 = 1 and x2 = −1.