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x^2+4x-5=0

x^2+4x-5=0 equation

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Numerical solution:

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The solution

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x  + 4*x - 5 = 0
(x2+4x)−5=0\left(x^{2} + 4 x\right) - 5 = 0
Simplify
Detail solution
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=4b = 4
c=−5c = -5
, then
D = b^2 - 4 * a * c = 

(4)^2 - 4 * (1) * (-5) = 36

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

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

or
x1=1x_{1} = 1
x2=−5x_{2} = -5
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=4p = 4
q=caq = \frac{c}{a}
q=−5q = -5
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−4x_{1} + x_{2} = -4
x1x2=−5x_{1} x_{2} = -5
The graph
05-20-15-10-51015-200200
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-5 + 1
−5+1-5 + 1 
=
-4
−4-4 
product
-5
−5-5 
=
-5
−5-5 
-5
Rapid solution [src] 
x1 = -5
x1=−5x_{1} = -5 
x2 = 1
x2=1x_{2} = 1 
x2 = 1
Numerical answer [src] 
x1 = 1.0
x2 = -5.0
x2 = -5.0
The graph
x^2+4x-5=0 equation
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