Question

(X-5)^2 +X-8=X+19
Resuelve esta ecuación cuadratica

Answer 1

Calcular.

Aplicas .
Productos notables.
(a - b)² = a² - 2ab + b²

(x - 5)² + x - 8 = x + 19
x² - 2(x)(5) + 5² + x - 8 = x + 19
x² - 10x + 25 + x - 8 = x + 19
x² - 9x + 17 = x + 19
x² - 9x + 17 - x - 19 = 0
x² - 10x - 2 = 0

a = 1
b = - 10
c = - 2

Formula.

x = [ - b +/-√(b² - 4ac)]/2a

x =[- (- 10) +/-√(- 10)² - 4(1)(- 2)]/2(1)
x = [10 +/- √(100+ 8)]/2
x = [10 + /-√108]/2
x = [ 10 +/- √(36 * 3)]/2
x = [10 +/- 6√3]/2
x₁ = (10 + 6√3)/2      Sacas factor comun 2
x₁ = 2(5 + 3√3)/2        Simplificas el 2
x₁ = 5 + 3√3
   o
x₂ = 5 - 3√3

Respuesta.
(5 + 3√3 , 5 - 3√3)