10^-3.68=x^2/(0.5-x)

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Solution for 10^-3.68=x^2/(0.5-x) equation: 


D( x )

0.5-x = 0

0.5-x = 0

0.5-x = 0

0.5-x = 0 // - 0.5

-x = -0.5 // * -1

x = 0.5

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

10^-3.68 = (x^2)/(0.5-x) // - (x^2)/(0.5-x)

10^-3.68-((x^2)/(0.5-x)) = 0

(-1*x^2)/(0.5-x)+10^-3.68 = 0

(-1*x^2)/(0.5-x)+(10^-3.68*(0.5-x))/(0.5-x) = 0

10^-3.68*(0.5-x)-1*x^2 = 0

0.5*10^-3.68-x^2-10^-3.68*x = 0

0.5*10^-3.68-x^2-10^-3.68*x = 0

0.5*10^-3.68-x^2-10^-3.68*x = 0

DELTA = (-10^-3.68)^2-(-1*0.5*4*10^-3.68)

DELTA = 10^-7.36+2*10^-3.68

DELTA = 0.0004179

DELTA > 0

x = (10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-1*2) or x = (10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-1*2)

x = (10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2) or x = (10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2)

(x-((10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2)))*(x-((10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2))) = 0

((x-((10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2)))*(x-((10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2))))/(0.5-x) = 0

((x-((10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2)))*(x-((10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2))))/(0.5-x) = 0 // * 0.5-x

(x-((10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2)))*(x-((10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2))) = 0

( x-((10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2)) )

x-((10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2)) = 0 // + (10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2)

x = (10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2)

( x-((10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2)) )

x-((10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2)) = 0 // + (10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2)

x = (10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2)

x in { (10^-3.68+(10^-7.36+2*10^-3.68)^(1/2))/(-2), (10^-3.68-(10^-7.36+2*10^-3.68)^(1/2))/(-2) }

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