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x^2+10x=0

x^2+10x=0 equation

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Numerical solution:

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The solution

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 2           
x  + 10*x = 0
x2+10x=0x^{2} + 10 x = 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=10b = 10
c=0c = 0
, then
D = b^2 - 4 * a * c = 

(10)^2 - 4 * (1) * (0) = 100

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

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

or
x1=0x_{1} = 0
x2=−10x_{2} = -10
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=10p = 10
q=caq = \frac{c}{a}
q=0q = 0
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=−10x_{1} + x_{2} = -10
x1x2=0x_{1} x_{2} = 0
The graph
05-30-25-20-15-10-51510-250250
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-10
−10-10 
=
-10
−10-10 
product
-10*0
−0- 0 
=
0
00 
0
Rapid solution [src] 
x1 = -10
x1=−10x_{1} = -10 
x2 = 0
x2=0x_{2} = 0 
x2 = 0
Numerical answer [src] 
x1 = -10.0
x2 = 0.0
x2 = 0.0
The graph
x^2+10x=0 equation
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