1/4-x^2>=0 inequation

Given the inequality:
$$\frac{1}{4} - x^{2} \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{1}{4} - x^{2} = 0$$
Solve:
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
$$a = -1$$
$$b = 0$$
$$c = \frac{1}{4}$$
, then

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

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

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

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

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

or
$$x_{1} = - \frac{1}{2}$$
$$x_{2} = \frac{1}{2}$$
$$x_{1} = - \frac{1}{2}$$
$$x_{2} = \frac{1}{2}$$
$$x_{1} = - \frac{1}{2}$$
$$x_{2} = \frac{1}{2}$$
This roots
$$x_{1} = - \frac{1}{2}$$
$$x_{2} = \frac{1}{2}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{2} + - \frac{1}{10}$$
=
$$- \frac{3}{5}$$
substitute to the expression
$$\frac{1}{4} - x^{2} \geq 0$$
$$\frac{1}{4} - \left(- \frac{3}{5}\right)^{2} \geq 0$$

-11      
---- >= 0
100      

but

-11     
---- < 0
100     

Then
$$x \leq - \frac{1}{2}$$
no execute
one of the solutions of our inequality is:
$$x \geq - \frac{1}{2} \wedge x \leq \frac{1}{2}$$

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        /     \  
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       x1      x2