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2*x^2+7=0

2*x^2+7=0 equation

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Numerical solution:

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The solution

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   2        
2*x  + 7 = 0
2x2+7=02 x^{2} + 7 = 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=2a = 2
b=0b = 0
c=7c = 7
, then
D = b^2 - 4 * a * c = 

(0)^2 - 4 * (2) * (7) = -56

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=14i2x_{1} = \frac{\sqrt{14} i}{2}
x2=−14i2x_{2} = - \frac{\sqrt{14} i}{2}
Vieta's Theorem
rewrite the equation
2x2+7=02 x^{2} + 7 = 0
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2+72=0x^{2} + \frac{7}{2} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=0p = 0
q=caq = \frac{c}{a}
q=72q = \frac{7}{2}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=0x_{1} + x_{2} = 0
x1x2=72x_{1} x_{2} = \frac{7}{2}
The graph
-3.5-3.0-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.53.03.5020
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
      ____       ____
  I*\/ 14    I*\/ 14 
- -------- + --------
     2          2
−14i2+14i2- \frac{\sqrt{14} i}{2} + \frac{\sqrt{14} i}{2} 
=
0
00 
product
     ____      ____
-I*\/ 14   I*\/ 14 
----------*--------
    2         2
−14i214i2- \frac{\sqrt{14} i}{2} \frac{\sqrt{14} i}{2} 
=
7/2
72\frac{7}{2} 
7/2
Rapid solution [src] 
          ____ 
     -I*\/ 14  
x1 = ----------
         2
x1=−14i2x_{1} = - \frac{\sqrt{14} i}{2} 
         ____
     I*\/ 14 
x2 = --------
        2
x2=14i2x_{2} = \frac{\sqrt{14} i}{2} 
x2 = sqrt(14)*i/2
Numerical answer [src] 
x1 = 1.87082869338697*i
x2 = -1.87082869338697*i
x2 = -1.87082869338697*i
The graph
2*x^2+7=0 equation
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