sin(sqrt(x))<=0 inequation

Given the inequality:
$$\sin{\left(\sqrt{x} \right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(\sqrt{x} \right)} = 0$$
Solve:
Given the equation
$$\sin{\left(\sqrt{x} \right)} = 0$$
transform
$$\sin{\left(\sqrt{x} \right)} - 1 = 0$$
$$\sin{\left(\sqrt{x} \right)} - 1 = 0$$
Do replacement
$$w = \sin{\left(\sqrt{x} \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = 1$$
We get the answer: w = 1
do backward replacement
$$\sin{\left(\sqrt{x} \right)} = w$$
substitute w:
$$x_{1} = 0$$
$$x_{2} = \pi^{2}$$
$$x_{1} = 0$$
$$x_{2} = \pi^{2}$$
This roots
$$x_{1} = 0$$
$$x_{2} = \pi^{2}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 0$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$\sin{\left(\sqrt{x} \right)} \leq 0$$
$$\sin{\left(\sqrt{- \frac{1}{10}} \right)} \leq 0$$

      /  ____\     
      |\/ 10 |     
I*sinh|------| <= 0
      \  10  /     
     

Then
$$x \leq 0$$
no execute
one of the solutions of our inequality is:
$$x \geq 0 \wedge x \leq \pi^{2}$$

         _____  
        /     \  
-------•-------•-------
       x_1      x_2