x=2k/(x+2)

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Solution for x=2k/(x+2) equation:


D( x )

x+2 = 0

x+2 = 0

x+2 = 0

x+2 = 0 // - 2

x = -2

x in (-oo:-2) U (-2:+oo)

x = (2*k)/(x+2) // - (2*k)/(x+2)

x-((2*k)/(x+2)) = 0

x-2*k*(x+2)^-1 = 0

(-2*k)/(x+2)+x = 0

(-2*k)/(x+2)+(x*(x+2))/(x+2) = 0

x*(x+2)-2*k = 0

x^2-2*k+2*x = 0

(x^2-2*k+2*x)/(x+2) = 0

(x^2-2*k+2*x)/(x+2) = 0 // * x+2

x^2-2*k+2*x = 0

x^2-2*k+2*x = 0

DELTA = 2^2-(-2*1*4*k)

DELTA = 8*k+4

8*k+4 = 0

8*k+4 = 0 // - 4

8*k = -4 // : 8

k = -4/8

k = -1/2

DELTA = 0 <=> t_3 = -1/2

x = -2/(1*2) i k = -1/2

x = -1 i k = -1/2

( x = ((8*k+4)^(1/2)-2)/(1*2) or x = (-(8*k+4)^(1/2)-2)/(1*2) ) i k > -1/2

( x = ((8*k+4)^(1/2)-2)/2 or x = (-((8*k+4)^(1/2)+2))/2 ) i k > -1/2

k+1/2 > 0

k+1/2 > 0 // - 1/2

k > -1/2

x in { -1, ((8*k+4)^(1/2)-2)/2, (-((8*k+4)^(1/2)+2))/2 }

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