50=(0.5+2x)^2/((0.25-x)^2)

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Solution for 50=(0.5+2x)^2/((0.25-x)^2) equation: 


D( x )

(0.25-x)^2 = 0

(0.25-x)^2 = 0

(0.25-x)^2 = 0

0.25-x = 0 // - 0.25

-x = -0.25 // * -1

x = 0.25

x in (-oo:0.25) U (0.25:+oo)

50 = ((2*x+0.5)^2)/((0.25-x)^2) // - ((2*x+0.5)^2)/((0.25-x)^2)

50-(((2*x+0.5)^2)/((0.25-x)^2)) = 0

(-1*(2*x+0.5)^2)/((0.25-x)^2)+50 = 0

(-1*(2*x+0.5)^2)/((0.25-x)^2)+(50*(0.25-x)^2)/((0.25-x)^2) = 0

50*(0.25-x)^2-1*(2*x+0.5)^2 = 0

46*x^2-27*x+2.875 = 0

46*x^2-27*x+2.875 = 0

46*x^2-27*x+2.875 = 0

DELTA = (-27)^2-(2.875*4*46)

DELTA = 200

DELTA > 0

x = (200^(1/2)+27)/(2*46) or x = (27-200^(1/2))/(2*46)

x = (10*2^(1/2)+27)/92 or x = (27-10*2^(1/2))/92

(x-((27-10*2^(1/2))/92))*(x-((10*2^(1/2)+27)/92)) = 0

((x-((27-10*2^(1/2))/92))*(x-((10*2^(1/2)+27)/92)))/((0.25-x)^2) = 0

((x-((27-10*2^(1/2))/92))*(x-((10*2^(1/2)+27)/92)))/((0.25-x)^2) = 0 // * (0.25-x)^2

(x-((27-10*2^(1/2))/92))*(x-((10*2^(1/2)+27)/92)) = 0

( x-((10*2^(1/2)+27)/92) )

x-((10*2^(1/2)+27)/92) = 0 // + (10*2^(1/2)+27)/92

x = (10*2^(1/2)+27)/92

( x-((27-10*2^(1/2))/92) )

x-((27-10*2^(1/2))/92) = 0 // + (27-10*2^(1/2))/92

x = (27-10*2^(1/2))/92

x in { (10*2^(1/2)+27)/92, (27-10*2^(1/2))/92 }

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