Mister Exam
8*p^2-8*p*(p+5)<=100 inequation
The solution
You have entered
[src]
2 8*p - 8*p*(p + 5) <= 100
$$8 p^{2} - 8 p \left(p + 5\right) \leq 100$$
8*p^2 - 8*p*(p + 5) <= 100
Detail solution
Given the inequality:
$$8 p^{2} - 8 p \left(p + 5\right) \leq 100$$
To solve this inequality, we must first solve the corresponding equation:
$$8 p^{2} - 8 p \left(p + 5\right) = 100$$
Solve:
$$x_{1} = -2.5$$
$$x_{1} = -2.5$$
This roots
$$x_{1} = -2.5$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2.5 + - \frac{1}{10}$$
=
$$-2.6$$
substitute to the expression
$$8 p^{2} - 8 p \left(p + 5\right) \leq 100$$
$$8 p^{2} - 8 p \left(p + 5\right) \leq 100$$
Then
$$x \leq -2.5$$
no execute
the solution of our inequality is:
$$x \geq -2.5$$
$$8 p^{2} - 8 p \left(p + 5\right) \leq 100$$
To solve this inequality, we must first solve the corresponding equation:
$$8 p^{2} - 8 p \left(p + 5\right) = 100$$
Solve:
$$x_{1} = -2.5$$
$$x_{1} = -2.5$$
This roots
$$x_{1} = -2.5$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$-2.5 + - \frac{1}{10}$$
=
$$-2.6$$
substitute to the expression
$$8 p^{2} - 8 p \left(p + 5\right) \leq 100$$
$$8 p^{2} - 8 p \left(p + 5\right) \leq 100$$
2
8*p - 8*p*(5 + p) <= 100
Then
$$x \leq -2.5$$
no execute
the solution of our inequality is:
$$x \geq -2.5$$
_____
/
-------•-------
x1
Rapid solution 2
[src]
[-5/2, oo)
$$x\ in\ \left[- \frac{5}{2}, \infty\right)$$
x in Interval(-5/2, oo)
Rapid solution
[src]
And(-5/2 <= p, p < oo)
$$- \frac{5}{2} \leq p \wedge p < \infty$$
(-5/2 <= p)∧(p < oo)