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

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Solution for 0.802=x^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)

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

0.802-((x^2)/((0.5-x)^2)) = 0

(-1*x^2)/((0.5-x)^2)+0.802 = 0

(-1*x^2)/((0.5-x)^2)+(0.802*(0.5-x)^2)/((0.5-x)^2) = 0

0.802*(0.5-x)^2-1*x^2 = 0

0.802*0.5^2-0.198*x^2-0.802*x = 0

0.802*0.5^2-0.198*x^2-0.802*x = 0

0.802*0.5^2-0.198*x^2-0.802*x = 0

DELTA = (-0.802)^2-(-0.198*0.802*4*0.5^2)

DELTA = 0.802^2+0.635184*0.5^2

DELTA = 0.802

DELTA > 0

x = ((0.802^2+0.635184*0.5^2)^(1/2)+0.802)/(-0.198*2) or x = (0.802-(0.802^2+0.635184*0.5^2)^(1/2))/(-0.198*2)

x = -2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802) or x = -2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2))

(x+2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802))*(x+2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2))) = 0

((x+2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802))*(x+2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2))))/((0.5-x)^2) = 0

((x+2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802))*(x+2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2))))/((0.5-x)^2) = 0 // * (0.5-x)^2

(x+2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802))*(x+2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2))) = 0

( x+2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802) )

x+2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802) = 0 // - 2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802)

x = -(2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802))

x = -2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802)

( x+2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2)) )

x+2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2)) = 0 // - 2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2))

x = -(2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2)))

x = -2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2))

x in { -2.52525253*((0.802^2+0.635184*0.5^2)^(1/2)+0.802), -2.52525253*(0.802-(0.802^2+0.635184*0.5^2)^(1/2)) }

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