0,1x^2<=10 inequation

Given the inequality:
$$\frac{x^{2}}{10} \leq 10$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{x^{2}}{10} = 10$$
Solve:
Move right part of the equation to
left part with negative sign.

The equation is transformed from
$$\frac{x^{2}}{10} = 10$$
to
$$\frac{x^{2}}{10} - 10 = 0$$
This equation is of the form

a*x^2 + b*x + c = 0

A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = \frac{1}{10}$$
$$b = 0$$
$$c = -10$$
, then

D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1/10) * (-10) = 4

Because D > 0, then the equation has two roots.

x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = 10$$
$$x_{2} = -10$$
$$x_{1} = 10$$
$$x_{2} = -10$$
$$x_{1} = 10$$
$$x_{2} = -10$$
This roots
$$x_{2} = -10$$
$$x_{1} = 10$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$-10 + - \frac{1}{10}$$
=
$$- \frac{101}{10}$$
substitute to the expression
$$\frac{x^{2}}{10} \leq 10$$
$$\frac{\left(- \frac{101}{10}\right)^{2}}{10} \leq 10$$

10201      
----- <= 10
 1000      

but

10201      
----- >= 10
 1000      

Then
$$x \leq -10$$
no execute
one of the solutions of our inequality is:
$$x \geq -10 \wedge x \leq 10$$

         _____  
        /     \  
-------•-------•-------
       x2      x1