SOLUTION: If {{{ (x+k)^2= x^2 +22x+k^2 }}} for all real numbers x, then what does k equal?

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Question 997912: If +%28x%2Bk%29%5E2=+x%5E2+%2B22x%2Bk%5E2+ for all real numbers x, then what does k equal?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If +%28x%2Bk%29%5E2=+x%5E2+%2B22x%2Bk%5E2+for all real numbers x, then what does k equal?
:
From completing the square procedure we know that k^2 = half the coefficient of x squared.
k^2 = (22%2F2)^2 = 121
k = sqrt%28121%29
k = 11
:
Check: FOIL(x+11)(x+11) = x^2 + 11x + 11x + 121 = x^2 + 22x + 121