(0.4-2x)^2/x*x=49.5

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Solution for (0.4-2x)^2/x*x=49.5 equation:


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

x*(((0.4-(2*x))^2)/x) = 49.5 // - 49.5

x*(((0.4-(2*x))^2)/x)-49.5 = 0

x*(((0.4-2*x)^2)/x)-49.5 = 0

(x*(0.4-2*x)^2)/x-49.5 = 0

(x*(0.4-2*x)^2)/x+(-49.5*x)/x = 0

x*(0.4-2*x)^2-49.5*x = 0

4*x^3-1.6*x^2-49.34*x = 0

4*x^3-1.6*x^2-49.34*x = 0

x*(4*x^2-1.6*x-49.34) = 0

4*x^2-1.6*x-49.34 = 0

DELTA = (-1.6)^2-(-49.34*4*4)

DELTA = 1.6^2+789.44

DELTA = 792

DELTA > 0

x = ((1.6^2+789.44)^(1/2)+1.6)/(2*4) or x = (1.6-(1.6^2+789.44)^(1/2))/(2*4)

x = ((1.6^2+789.44)^(1/2)+1.6)/8 or x = (1.6-(1.6^2+789.44)^(1/2))/8

x*(x-((1.6-(1.6^2+789.44)^(1/2))/8))*(x-(((1.6^2+789.44)^(1/2)+1.6)/8)) = 0

(x*(x-((1.6-(1.6^2+789.44)^(1/2))/8))*(x-(((1.6^2+789.44)^(1/2)+1.6)/8)))/x = 0

(x*(x-((1.6-(1.6^2+789.44)^(1/2))/8))*(x-(((1.6^2+789.44)^(1/2)+1.6)/8)))/x = 0 // * x

x*(x-((1.6-(1.6^2+789.44)^(1/2))/8))*(x-(((1.6^2+789.44)^(1/2)+1.6)/8)) = 0

( x-(((1.6^2+789.44)^(1/2)+1.6)/8) )

x-(((1.6^2+789.44)^(1/2)+1.6)/8) = 0 // + ((1.6^2+789.44)^(1/2)+1.6)/8

x = ((1.6^2+789.44)^(1/2)+1.6)/8

( x-((1.6-(1.6^2+789.44)^(1/2))/8) )

x-((1.6-(1.6^2+789.44)^(1/2))/8) = 0 // + (1.6-(1.6^2+789.44)^(1/2))/8

x = (1.6-(1.6^2+789.44)^(1/2))/8

( x )

x = 0

x in { 0}

x in { ((1.6^2+789.44)^(1/2)+1.6)/8, (1.6-(1.6^2+789.44)^(1/2))/8 }

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