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x^2+81=0 equation

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Numerical solution:

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The solution

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 2         
x  + 81 = 0
x2+81=0x^{2} + 81 = 0
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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=0b = 0
c=81c = 81
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (81) = -324

Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)

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

or
x1=9ix_{1} = 9 i
x2=−9ix_{2} = - 9 i
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=81q = 81
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=81x_{1} x_{2} = 81
Sum and product of roots [src] 
sum
-9*I + 9*I
−9i+9i- 9 i + 9 i 
=
0
00 
product
-9*I*9*I
−9i9i- 9 i 9 i 
=
81
8181 
81
Rapid solution [src] 
x1 = -9*I
x1=−9ix_{1} = - 9 i 
x2 = 9*I
x2=9ix_{2} = 9 i 
x2 = 9*i
Numerical answer [src] 
x1 = 9.0*i
x2 = -9.0*i
x2 = -9.0*i
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