What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? use u substitution and the quadratic formula to solve.
a) x= -8+5 square root 2
b) x=-6+5 square root 2
c) x= -4+5 square root 2
d) x= -2+5 square root 2

(x + 2)² + 12(x + 2) – 14 = 0

(x +2) ² we use the formula (a+b)² = a² + 2ab + b²

(x² + 2*2*x + 4 ) + (12*x + 12 * 2 ) - 14 = 0
(x² + 4x + 4) + (12x + 24) - 14 = 0
x² + 4x + 4 + 12x + 24 - 14 = 0

we sort expressions
x² + 4x + 12x + 4 + 24 - 14 = 0

reduce
x² + 16x + 14 = 0 

a = 1    b = 16     c=14

Δ = b² - 4ac = 16² - 4*1*14 = 256 - 56 = 200
√Δ = √(2*10*10) = 10√2





Answer A

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