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Q: What is x2 plus 6x plus 9 equals x plus 3?

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x2 + 6x + 12 = 0 x2 + 6x + 9 = -3 (x + 3)2 = -3 x + 3 = ± √-3 x = -3 ± i√3

x2 + 6x - 2 = 0 x2 + 6x + 9 = 13 (x + 3)2 = 13 x + 3 = ± √13 x = -3 ± √13

(3, -21)

x2 + 6x = 7 ⇒ x2 + 6x + 9 = 7 + 9 ⇒ (x + 3)2 = 16 ⇒ x + 3 = ±4 ⇒ x = -7 or 1

y = x2 - 6x + 2 y = x2 - 6x + 9 - 7 y = (x - 3)2 - 7

x2 + 6x + 1 = 0 x2 + 6x + 9 = 8 (x + 3)2 = 8 x + 3 = ± 2√2 x + 3 = -3 ± 2√2 x ∈ {-3 - 2√2, -3 + 2√2}

(x - 3)(x - 2)

x2-6x+9 = (x-3)(x-3) when factorised.

x2 - 6x = 16 ∴ x2 - 6x + 9 = 25 ∴ (x - 3)2 = 25 ∴ x - 3 = 25 ∴ x = 28

x2 +6x = 27 x2 + 6x - 27 = 0 x2 + 9x - 3x - 27 = 0 x(x + 9) - 3(x + 9) =0 (x - 3)(x + 9) = 0 So x can equal 3 or -9.

x2 + 6x - 27 = (x + 9)(x - 3)

(-3,-1)

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