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Write the the function f(x)=-2x2-12x+22 in the form f(x)=a(x-p)2+q by completing the square:

1. We take out the coefficient of x2, a, as a factor from the first two terms:

f(x)=(x2+ x)+22

2. Then we add half of the coefficient of x squared, (b2)2, inside the bracket and subtract it outside a times, a(b2)2.

f(x)=(x2+x+)+22-

3. Then we factorize the bracket and simplify outside the bracket.

f(x)=(x+)2+

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Completing the square