First, expand (x-2)^{2}:

= (x-2)(x-2),

= x^{2} - 2x - 2x + 4

= x^{2} - 4x + 4

Add on the +7:

= x^{2} - 4x + 11

complete the square

= (x - 2)^{2} - 4 + 11

= (x - 2)^{2} + 7

when the graph has a minumum value, (x - 2) = 0,

so x = 2

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