Question

Resolva simplificando e determine o conjunto solução.
a) x.(x-2) = 2.(x+6)

Answer 1

$x.(x-2) = 2.(x+6)\\ \\ x^2-2x=2x+12\\ \\ x^{2} -4x-12=0\\ \\ \Delta=(-4)^2-4.1.(-12)=16+48=64\\ \\ x=\frac{4 \pm\sqrt{64}}{2}=\frac{4 \pm 8}{2}\\ \\ x_1=-2\\ \\ x_2=6$

Answer 2

a) x.(x-2) = 2.(x+6) => x.(x-2) = 2.(x+6) =  x² - 2x = 2x + 12 =  x² - 2x - 2x - 12 = 0 =>
 x² - 4x - 12 = 0, p/ a = 1; b = -4 e c = -12
Δ = (-4)² - 4(1)(-12) = 16 + 48 = 64
x' = [-(-4) + √64]/2.1 = (4 + 8)/2 = 6
x" = [-(-4) - √64]/2.1 = (4 - 8)/2 = -2
S = {-2, 6}