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# Completing The Square

Learn how to eliminate the linear term and see through messy quadratics. You’ll know just how high to shoot your three-pointer to avoid tall defenders.

As \(x\) ranges over all real values, what is the minimum value of \( x^ 2 + 28 x + 313 \)?

As \(x\) ranges over all real values, what is the smallest integer value of

\[ \frac{ x^2 + 22x + 333} { 11} ? \]

**Details and assumptions**

Note that we are not asking for the value of \(x\).

If the solution of the equation \[x^2+6x-1=0\] is \(x=a \pm \sqrt{b}\), what is \(a+b\)?

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