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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 two roots.
x1 = (-b + sqrt(D)) / (2*a)

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

or
x1=142x_{1} = \frac{\sqrt{14}}{2}
x2=−142x_{2} = - \frac{\sqrt{14}}{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
05-15-10-51015-500500
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
        ____ 
     -\/ 14  
x1 = --------
        2
x1=−142x_{1} = - \frac{\sqrt{14}}{2} 
       ____
     \/ 14 
x2 = ------
       2
x2=142x_{2} = \frac{\sqrt{14}}{2} 
x2 = sqrt(14)/2
Sum and product of roots [src] 
sum
    ____     ____
  \/ 14    \/ 14 
- ------ + ------
    2        2
−142+142- \frac{\sqrt{14}}{2} + \frac{\sqrt{14}}{2} 
=
0
00 
product
   ____    ____
-\/ 14   \/ 14 
--------*------
   2       2
−142142- \frac{\sqrt{14}}{2} \frac{\sqrt{14}}{2} 
=
-7/2
−72- \frac{7}{2} 
-7/2
Numerical answer [src] 
x1 = -1.87082869338697
x2 = 1.87082869338697
x2 = 1.87082869338697
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