x2+6x+9 = x+3
x2+6x-x+9-3 = 0
x2+5x+6 = 0
Solve by factoring or with the help of the quadratic equation formula:
(x+3)(x+2) = 0
Therefore: x = -3 or x = -2
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x2 + 6x = 7 ⇒ x2 + 6x + 9 = 7 + 9 ⇒ (x + 3)2 = 16 ⇒ x + 3 = ±4 ⇒ x = -7 or 1
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}
y = x2 - 6x + 2 y = x2 - 6x + 9 - 7 y = (x - 3)2 - 7
x2-6x+9 = (x-3)(x-3) when factorised.