+128406 x ( x + 6) > 16 + 2x
x^2 + 6x > 16 + 2x rearrange as
x^2 + 4x - 16 > 0
Solve this as an equality
x^2 + 4x - 16 = 0 complete the square on x
x^2 + 4x + 4 = 16 + 4
(x + 2)^2 = 20 take both roots
x + 2 = ±sqrt 20
x = sqrt 20 - 2 ≈ 2sqrt (5) - 2 ≈ 2.47 or x = -sqrt 20 - 2 = -2sqrt (5) - 2 ≈ -6.47
Note that the intervals that possibly solve the original inequality are x =
(-inf , ≈ -6.47) or ( ≈ -6.47 , ≈ 2.47) or ( ≈ 2,47 , inf)
If we let x = 0 ,the middle interval does not solve the original inequality
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So.....the solutions are ( -inf , -2sqrt (2) - 2 ) and ( 2sqrt (5) -2 , inf)
