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Consider the equation y = x2 + 6x - 2
This is similar to the expression (x+3)2.
(x+3)2 = x2 + 6x + 9
Therefore y = (x + 3)2 - 11
The key here is that you can always rewrite a quadratic as (x + a)2 - b, where a is half the x coefficient, and b is the number you need to subtract to make up the correct constant.
Now to solve the equation when it is equal to 0:
(x+3)2 - 11 = 0
Add 11 to both sides: (x+3)2 = 11
Square root: x + 3 = +-sqrt11 (remember that square rooting always produces a positive answer and a negative answer)
Subtract 3: x = -3 + sqrt 11 or -3 - sqrt11
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