Question

Resolva a equação x²+2x-8=0

Answer 1

x² + 2x - 8 = 0
Delta = b² - 4ac
Delta = 4 - 4(1)(-8)
Delta = 4 + 32
Delta = 36

X = (-b +- raiz delta) / 2a
X = (-2 +- 6) / 2
x' = (-2 + 6) / 2 = 4/2 = 2
x" = (-2 - 6) / 2 = -8/2 = -4

Answer 2

Método de completar quadrados:

$x^{2} +2-8=0 \\ \\ x^{2} +2x+1-8=0+1 \\ \\ (x+1)^{2} -8=1 \\ \\ (x+1)^{2} =1+8 \\ \\ (x+1)^{2}=9 \\ \\ x+1=+- \sqrt{9} \\ \\ x+1=+-3 \\ -------------------------- \\ x+1=3 \\ x=3-1 \\ x=\boxed{2} \\ \\ x+1=-3 \\ x=3-1 \\ x=\boxed{-4}$