Question

What are the solutions of the equation (x + 2)2 + 12(x + 2) – 14 = 0? Use u substitution and the quadratic formula to solve.

Answer 1

Answer:

answer is A

Step-by-step explanation:

Answer 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

$x_{1} = \frac{-b - \sqrt{delty} }{2a} = \frac{-16 - 10 \sqrt{2} }{2*1} = \frac{-8 -5 \sqrt{2} }{1} = -8 -5 \sqrt{2}$

$x_{2} = \frac{-b + \sqrt{delty} }{2a} = \frac{-16+ 10 \sqrt{5} }{2*1} = \frac{-8 + 5 \sqrt{2} }{1} = -8 + 5 \sqrt{2}$

Answer A