2.5=((2x)^2)/((1-2x)^2)

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Solution for 2.5=((2x)^2)/((1-2x)^2) equation:


D( x )

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

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

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

(1-2*x)^2 = 0

1-2*x = 0 // - 1

-2*x = -1 // : -2

x = -1/(-2)

x = 1/2

x in (-oo:1/2) U (1/2:+oo)

2.5 = ((2*x)^2)/((1-(2*x))^2) // - ((2*x)^2)/((1-(2*x))^2)

2.5-(((2*x)^2)/((1-(2*x))^2)) = 0

2.5-(((2*x)^2)/((1-2*x)^2)) = 0

(-1*4*x^2)/((1-2*x)^2)+2.5 = 0

(-1*4*x^2)/((1-2*x)^2)+(2.5*(1-2*x)^2)/((1-2*x)^2) = 0

2.5*(1-2*x)^2-1*4*x^2 = 0

6*x^2-10*x+2.5 = 0

6*x^2-10*x+2.5 = 0

6*x^2-10*x+2.5 = 0

DELTA = (-10)^2-(2.5*4*6)

DELTA = 40

DELTA > 0

x = (40^(1/2)+10)/(2*6) or x = (10-40^(1/2))/(2*6)

x = (2*10^(1/2)+10)/12 or x = (10-2*10^(1/2))/12

(x-((10-2*10^(1/2))/12))*(x-((2*10^(1/2)+10)/12)) = 0

((x-((10-2*10^(1/2))/12))*(x-((2*10^(1/2)+10)/12)))/((1-2*x)^2) = 0

((x-((10-2*10^(1/2))/12))*(x-((2*10^(1/2)+10)/12)))/((1-2*x)^2) = 0 // * (1-2*x)^2

(x-((10-2*10^(1/2))/12))*(x-((2*10^(1/2)+10)/12)) = 0

( x-((10-2*10^(1/2))/12) )

x-((10-2*10^(1/2))/12) = 0 // + (10-2*10^(1/2))/12

x = (10-2*10^(1/2))/12

( x-((2*10^(1/2)+10)/12) )

x-((2*10^(1/2)+10)/12) = 0 // + (2*10^(1/2)+10)/12

x = (2*10^(1/2)+10)/12

x in { (10-2*10^(1/2))/12, (2*10^(1/2)+10)/12 }

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