x^2/(0.1-x)=0.09

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Solution for x^2/(0.1-x)=0.09 equation: 


D( x )

0.1-x = 0

0.1-x = 0

0.1-x = 0

0.1-x = 0 // - 0.1

-x = -0.1 // * -1

x = 0.1

x in (-oo:0.1) U (0.1:+oo)

(x^2)/(0.1-x) = 0.09 // - 0.09

(x^2)/(0.1-x)-0.09 = 0

(x^2)/(0.1-x)+(-0.09*(0.1-x))/(0.1-x) = 0

x^2-0.09*(0.1-x) = 0

x^2+0.09*x-0.009 = 0

x^2+0.09*x-0.009 = 0

x^2+0.09*x-0.009 = 0

DELTA = 0.09^2-(-0.009*1*4)

DELTA = 0.09^2+0.036

DELTA = 0.0441

DELTA > 0

x = ((0.09^2+0.036)^(1/2)-0.09)/(1*2) or x = (-(0.09^2+0.036)^(1/2)-0.09)/(1*2)

x = ((0.09^2+0.036)^(1/2)-0.09)/2 or x = (-((0.09^2+0.036)^(1/2)+0.09))/2

(x+((0.09^2+0.036)^(1/2)+0.09)/2)*(x-(((0.09^2+0.036)^(1/2)-0.09)/2)) = 0

((x+((0.09^2+0.036)^(1/2)+0.09)/2)*(x-(((0.09^2+0.036)^(1/2)-0.09)/2)))/(0.1-x) = 0

((x+((0.09^2+0.036)^(1/2)+0.09)/2)*(x-(((0.09^2+0.036)^(1/2)-0.09)/2)))/(0.1-x) = 0 // * 0.1-x

(x+((0.09^2+0.036)^(1/2)+0.09)/2)*(x-(((0.09^2+0.036)^(1/2)-0.09)/2)) = 0

( x+((0.09^2+0.036)^(1/2)+0.09)/2 )

x+((0.09^2+0.036)^(1/2)+0.09)/2 = 0 // - ((0.09^2+0.036)^(1/2)+0.09)/2

x = -(((0.09^2+0.036)^(1/2)+0.09)/2)

( x-(((0.09^2+0.036)^(1/2)-0.09)/2) )

x-(((0.09^2+0.036)^(1/2)-0.09)/2) = 0 // + ((0.09^2+0.036)^(1/2)-0.09)/2

x = ((0.09^2+0.036)^(1/2)-0.09)/2

x in { -(((0.09^2+0.036)^(1/2)+0.09)/2), ((0.09^2+0.036)^(1/2)-0.09)/2 }

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