I need to know the extrema value for the following equation, preferably by solving it with completing the square. f(x)=2x

^{2}-32x+74-
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First, 2 can be factored out, it does not change the extrema positions.

2*(x^{2}-16x+37); Let us from now operate on the trinomial inside the parentheses.

x2-16x+37=x^{2}-2*8*x+8^{2}-8^{2}+37=(x-8)^{2}-64+37=(x-8)^{2}-27.

This expression has a minimum when (x-8)^{2} is minimal. Since square of any number is nonnegative, the minimum is attained when (x-8)^{2}=0 or x=8. In this case f(8)=-27;