x^2/(x+4)^2=25

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Solution for x^2/(x+4)^2=25 equation: 


D( x )

(x+4)^2 = 0

(x+4)^2 = 0

(x+4)^2 = 0

x+4 = 0 // - 4

x = -4

x in (-oo:-4) U (-4:+oo)

(x^2)/((x+4)^2) = 25 // - 25

(x^2)/((x+4)^2)-25 = 0

(x^2)/((x+4)^2)+(-25*(x+4)^2)/((x+4)^2) = 0

x^2-25*(x+4)^2 = 0

-24*x^2-200*x-400 = 0

-24*x^2-200*x-400 = 0

-8*(3*x^2+25*x+50) = 0

3*x^2+25*x+50 = 0

DELTA = 25^2-(3*4*50)

DELTA = 25

DELTA > 0

x = (25^(1/2)-25)/(2*3) or x = (-25^(1/2)-25)/(2*3)

x = -10/3 or x = -5

-8*(x+5)*(x+10/3) = 0

(-8*(x+5)*(x+10/3))/((x+4)^2) = 0

(-8*(x+5)*(x+10/3))/((x+4)^2) = 0 // * (x+4)^2

-8*(x+5)*(x+10/3) = 0

( x+10/3 )

x+10/3 = 0 // - 10/3

x = -10/3

( x+5 )

x+5 = 0 // - 5

x = -5

x in { -10/3, -5 }

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