2.29=(2x)^2/(0.5-x)^2

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Solution for 2.29=(2x)^2/(0.5-x)^2 equation: 


D( x )

(0.5-x)^2 = 0

(0.5-x)^2 = 0

(0.5-x)^2 = 0

0.5-x = 0 // - 0.5

-x = -0.5 // * -1

x = 0.5

x in (-oo:0.5) U (0.5:+oo)

2.29 = ((2*x)^2)/((0.5-x)^2) // - ((2*x)^2)/((0.5-x)^2)

2.29-(((2*x)^2)/((0.5-x)^2)) = 0

(-1*4*x^2)/((0.5-x)^2)+2.29 = 0

(-1*4*x^2)/((0.5-x)^2)+(2.29*(0.5-x)^2)/((0.5-x)^2) = 0

2.29*(0.5-x)^2-1*4*x^2 = 0

0.5725-1.71*x^2-2.29*x = 0

0.5725-1.71*x^2-2.29*x = 0

0.5725-1.71*x^2-2.29*x = 0

DELTA = (-2.29)^2-(-1.71*0.5725*4)

DELTA = 2.29^2+3.9159

DELTA = 9.16

DELTA > 0

x = ((2.29^2+3.9159)^(1/2)+2.29)/(-1.71*2) or x = (2.29-(2.29^2+3.9159)^(1/2))/(-1.71*2)

x = -0.29239766*((2.29^2+3.9159)^(1/2)+2.29) or x = -0.29239766*(2.29-(2.29^2+3.9159)^(1/2))

(x+0.29239766*((2.29^2+3.9159)^(1/2)+2.29))*(x+0.29239766*(2.29-(2.29^2+3.9159)^(1/2))) = 0

((x+0.29239766*((2.29^2+3.9159)^(1/2)+2.29))*(x+0.29239766*(2.29-(2.29^2+3.9159)^(1/2))))/((0.5-x)^2) = 0

((x+0.29239766*((2.29^2+3.9159)^(1/2)+2.29))*(x+0.29239766*(2.29-(2.29^2+3.9159)^(1/2))))/((0.5-x)^2) = 0 // * (0.5-x)^2

(x+0.29239766*((2.29^2+3.9159)^(1/2)+2.29))*(x+0.29239766*(2.29-(2.29^2+3.9159)^(1/2))) = 0

( x+0.29239766*((2.29^2+3.9159)^(1/2)+2.29) )

x+0.29239766*((2.29^2+3.9159)^(1/2)+2.29) = 0 // - 0.29239766*((2.29^2+3.9159)^(1/2)+2.29)

x = -(0.29239766*((2.29^2+3.9159)^(1/2)+2.29))

x = -0.29239766*((2.29^2+3.9159)^(1/2)+2.29)

( x+0.29239766*(2.29-(2.29^2+3.9159)^(1/2)) )

x+0.29239766*(2.29-(2.29^2+3.9159)^(1/2)) = 0 // - 0.29239766*(2.29-(2.29^2+3.9159)^(1/2))

x = -(0.29239766*(2.29-(2.29^2+3.9159)^(1/2)))

x = -0.29239766*(2.29-(2.29^2+3.9159)^(1/2))

x in { -0.29239766*((2.29^2+3.9159)^(1/2)+2.29), -0.29239766*(2.29-(2.29^2+3.9159)^(1/2)) }

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