50 = (0.166 + x)²/(0.33 - x)²

50.(0.33 - x)² = (0.166 + x)²

50.(0.1089 - 0.66x + x²) = 0.027556 + 0.332x + x²

5.445 - 33x + 50x² = 0.027556 + 0.332x + x²

49x² - 33.332x + 5.417444 = 0

Polynomial like: ax² + bx + c, where:

a = 49

b = - 33.332

c = 5.417444

Δ = b² - 4ac (discriminant)

Δ = (- 33.332)² - 4.(49 * 5.417444)

Δ = 49.2032

Δ = 256 * 0.1922

x₁ = (- b - √Δ)/2a = (33.332 - 16√0.1922)/(2 * 49) = (16.666 - 8√0.1922)/49 ≈ 0.268546

x₂ = (- b + √Δ)/2a = (33.332 + 16√0.1922)/(2 * 49) = (16.666 + 8√0.1922)/49 ≈ 0.411699

Hola

Es más fácil de lo que parece

(0.166 + x)/(0.33 - x) = √50

(-0.166 - x)/(0.33 - x) = -√50

(-0.496 + 0.33 - x)/(0.33 - x) = -√50

[(-0.496 /(0.33 - x)] + 1 = -√50

[(-0.496 /(0.33 - x)] = -1 -√50

(0.496) /(0.33 - x) = 1 + √50

0.33 - x = 0.496 / (1 + √50)

x = 0.33 - ( 0.496 / (1 + √50) )

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De acuerdo al problema,

tenemos otra solución cambiando el signo de la raíz

https://www.youtube.com/watch?v=Y5zCUpQy6Rw