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Completing the square Method :

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The denominator is (x² + 6x + 11)² = 0.

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x² + 6x + 11 = 0

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Separate variables and constants aside by subtracting 11 from each side.

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x² + 6x = - 11

\ To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression. \

Here x coefficient = 6. So, (half the x coefficient)² = (6/2)²= 9.

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Add 9 to each side.

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x² + 6x + 9 = - 11 + 9

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x² + 2(x)(3) + 3² = - 2

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Apply Perfect Square Trinomial : u² + 2uv + v² = (u + v)².

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(x + 3)² = (i√2)²                                    [ i² = - 1]

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x + 3 = ± i√2

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x = - 3 ± i√2.

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The above imaginary numbers are not a critical numbers.

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The critical number of the function is x = - 3.

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