x/((1.09-x)^2)=2.01

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Solution for x/((1.09-x)^2)=2.01 equation: 


D( x )

(1.09-x)^2 = 0

(1.09-x)^2 = 0

(1.09-x)^2 = 0

1.09-x = 0 // - 1.09

-x = -1.09 // * -1

x = 1.09

x in (-oo:1.09) U (1.09:+oo)

x/((1.09-x)^2) = 2.01 // - 2.01

x/((1.09-x)^2)-2.01 = 0

x/((1.09-x)^2)+(-2.01*(1.09-x)^2)/((1.09-x)^2) = 0

x-2.01*(1.09-x)^2 = 0

5.3818*x-2.01*x^2-2.01*1.09^2 = 0

5.3818*x-2.01*x^2-2.01*1.09^2 = 0

5.3818*x-2.01*x^2-2.01*1.09^2 = 0

DELTA = 5.3818^2-(-2.01*(-2.01)*4*1.09^2)

DELTA = 5.3818^2-4*1.09^2*2.01^2

DELTA = 9.7636

DELTA > 0

x = ((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818)/(-2.01*2) or x = (-(5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818)/(-2.01*2)

x = -0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818) or x = 0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818)

(x+0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818))*(x-0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818)) = 0

((x+0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818))*(x-0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818)))/((1.09-x)^2) = 0

((x+0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818))*(x-0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818)))/((1.09-x)^2) = 0 // * (1.09-x)^2

(x+0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818))*(x-0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818)) = 0

( x+0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818) )

x+0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818) = 0 // - 0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818)

x = -(0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818))

x = -0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818)

( x-0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818) )

x-0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818) = 0 // + -0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818)

x = -(-0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818))

x = 0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818)

x in { -0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)-5.3818), 0.24875622*((5.3818^2-4*1.09^2*2.01^2)^(1/2)+5.3818) }

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