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x^2+2=x+2

x^2+2=x+2 equation

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Numerical solution:

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The solution

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

The equation is transformed from
x2+2=x+2x^{2} + 2 = x + 2
to
(−x−2)+(x2+2)=0\left(- x - 2\right) + \left(x^{2} + 2\right) = 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=−1b = -1
c=0c = 0
, then
D = b^2 - 4 * a * c = 

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

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

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

or
x1=1x_{1} = 1
x2=0x_{2} = 0
Vieta's Theorem
it is reduced quadratic equation
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−1p = -1
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=1x_{1} + x_{2} = 1
x1x2=0x_{1} x_{2} = 0
The graph
02468-8-6-4-210-10200-100
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
1
11 
=
1
11 
product
0
00 
=
0
00 
0
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
x2 = 1
x2=1x_{2} = 1 
x2 = 1
Numerical answer [src] 
x1 = 1.0
x2 = 0.0
x2 = 0.0
The graph
x^2+2=x+2 equation
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