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Solving inequalities/ (x+5)^2

(x+5)^2 inequation

A inequation with variable

The solution

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       2    
(x + 5)  > 0
(x+5)2>0\left(x + 5\right)^{2} > 0 
(x + 5)^2 > 0
Detail solution
Given the inequality:
(x+5)2>0\left(x + 5\right)^{2} > 0
To solve this inequality, we must first solve the corresponding equation:
(x+5)2=0\left(x + 5\right)^{2} = 0
Solve:
Expand the expression in the equation
(x+5)2=0\left(x + 5\right)^{2} = 0
We get the quadratic equation
x2+10x+25=0x^{2} + 10 x + 25 = 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:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D = b^2 - 4*a*c - it is the discriminant.
Because
a=1a = 1
b=10b = 10
c=25c = 25
, then
D = b^2 - 4 * a * c = 

(10)^2 - 4 * (1) * (25) = 0

Because D = 0, then the equation has one root.
x = -b/2a = -10/2/(1)

x1=−5x_{1} = -5
x1=−5x_{1} = -5
x1=−5x_{1} = -5
This roots
x1=−5x_{1} = -5
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
x0<x1x_{0} < x_{1}
For example, let's take the point
x0=x1−110x_{0} = x_{1} - \frac{1}{10}
=
−5+−110-5 + - \frac{1}{10}
=
−5110- \frac{51}{10}
substitute to the expression
(x+5)2>0\left(x + 5\right)^{2} > 0
(−5110+5)2>0\left(- \frac{51}{10} + 5\right)^{2} > 0
1/100 > 0

the solution of our inequality is:
x<−5x < -5
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       x1
Solving inequality on a graph
501234-8-7-6-5-4-3-2-1020
Rapid solution [src] 
And(x > -oo, x < oo, x != -5)
x>−∞∧x<∞∧x≠−5x > -\infty \wedge x < \infty \wedge x \neq -5 
(x > -oo)∧(x < oo)∧(Ne(x, -5))
Rapid solution 2 [src] 
(-oo, -5) U (-5, oo)
x in (−∞,−5)∪(−5,∞)x\ in\ \left(-\infty, -5\right) \cup \left(-5, \infty\right) 
x in Union(Interval.open(-oo, -5), Interval.open(-5, oo))
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