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

x = -8 + 5
`√(2)` or x = -8 - 5
`√(2)`

Explanation:

let u = x + 2

then (x + 2)2 + 12(x + 2) - 14 = 0 becomes:

u^2 + 12*u - 14 = 0

Quadratic Formula: u = -b/(2a) + root(b^2 - 4ac) / (2a)

u = -12/(2) + root (12^2 - 4*(-14) ) /(2)

u = -6 + root( 144 + 56) / 2

u = -6 + root(200)/2

u = -6 + 5 root(2)

or u = -6 - 5root(2)

replace u = x + 2

x + 2 = -6 + 5root(2)

x = -8 + 5 root(2) or x = -8 - 5root(2)

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Do Completing the Square:

u^2 + 12 u + 36 - 36 - 14 = 0

(u + 6)^2 - 50 = 0

(u + 6)^2 = 50

u + 6 = root(50)

u = -6 + 5root(2) OR u = -6 - 5root(2)

Answer 2

A

Explanation: