Question

como resolver equações como esta: (x+1)²=25 ?

Answer 1

$(x+1)^2=25 \\ (x+1).(x+1) = 25 \\ x^2 + x + x + 1 = 25 \\ x^2 + 2x + 1 - 25 = 0 \\ x^2 + 2x -24 = 0 \\ \\ \Delta = 2^2 - 4.1.(-24) \\ \Delta = 100 \\ \\ x = \frac{-2 \pm \sqrt{100} }{2.1} = \frac{-2 \pm 10}{2} \\ \\ x' = \frac{-2 + 10}{2} = \frac{8}{2} = 4 \\ \\ x'' = \frac{-2-10}{2} = \frac{-12}{2} = -6$

$\boxed{S = \{(-6;4)\}}$

Answer 2

(x+1)²=25

x² + 2x + 1 - 25 = 0

x² + 2x - 24 = 0

S = -2
P = -24

S = {-6, 4}