(x + 6)2 − 4(x + 6) − 12 = 0 Find all real solutions of the following equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION.)?

2 Answers

Oddman Profile
Oddman answered
You can factor this treating (x+6) as the variable.
  (x+6)^2 - 4(x+6) - 12 = 0
  ((x+6) - 6)((x+6) + 2) = 0    (factors of -12 that add to -4 are -6 and 2.)
  (x)(x+8) = 0

The solutions are {-8, 0}.
John McCann Profile
John McCann answered
Distribute, and I hope that first term is not squared. Or is it? Both ways. Squared first.

(X + 6)^2 - 4(X + 6) - 12 = 0

FOIL and distribute

X^2 + 12X + 36 - 4X - 24 - 12 = 0

gather terms

X^2 + 8X = 0

Obviously,

X = 0

X = - 8

------for this function
------now, the un-squared way

(X + 6) * 2 - 4 *(X + 6) - 12 = 0

distribute

2X + 12 - 4X - 24 - 12 = 0

gather like terms

- 2X  - 24 = 0

- 2X = 24

X = - 12

you check this one

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