Mister Exam

# x^2-29x<0 inequation

A inequation with variable

### The solution

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 2
x  - 29*x < 0
$$x^{2} - 29 x < 0$$
x^2 - 29*x < 0
Detail solution
Given the inequality:
$$x^{2} - 29 x < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x^{2} - 29 x = 0$$
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
$$a = 1$$
$$b = -29$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =

(-29)^2 - 4 * (1) * (0) = 841

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

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

or
$$x_{1} = 29$$
$$x_{2} = 0$$
$$x_{1} = 29$$
$$x_{2} = 0$$
$$x_{1} = 29$$
$$x_{2} = 0$$
This roots
$$x_{2} = 0$$
$$x_{1} = 29$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$x^{2} - 29 x < 0$$
$$\left(- \frac{1}{10}\right)^{2} - \frac{\left(-1\right) 29}{10} < 0$$
291
--- < 0
100    

but
291
--- > 0
100    

Then
$$x < 0$$
no execute
one of the solutions of our inequality is:
$$x > 0 \wedge x < 29$$
         _____
/     \
-------ο-------ο-------
x2      x1
Solving inequality on a graph
Rapid solution [src]
And(0 < x, x < 29)
$$0 < x \wedge x < 29$$
(0 < x)∧(x < 29)
Rapid solution 2 [src]
(0, 29)
$$x\ in\ \left(0, 29\right)$$
x in Interval.open(0, 29)