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x^2=-16

x^2=-16 equation

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Numerical solution:

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The solution

You have entered [src] 
 2      
x  = -16
x2=−16x^{2} = -16
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
x2=−16x^{2} = -16
to
x2+16=0x^{2} + 16 = 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=0b = 0
c=16c = 16
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (16) = -64

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=4ix_{1} = 4 i
x2=−4ix_{2} = - 4 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=16q = 16
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=16x_{1} x_{2} = 16
The graph
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.515.010.012.5200-100
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -4*I
x1=−4ix_{1} = - 4 i 
x2 = 4*I
x2=4ix_{2} = 4 i 
x2 = 4*i
Sum and product of roots [src] 
sum
-4*I + 4*I
−4i+4i- 4 i + 4 i 
=
0
00 
product
-4*I*4*I
−4i4i- 4 i 4 i 
=
16
1616 
16
Numerical answer [src] 
x1 = -4.0*i
x2 = 4.0*i
x2 = 4.0*i
The graph
x^2=-16 equation
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