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what is the complete square of z^2+22z+c

idk how to complete the square any help  z^2+22z+c

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2 Answers

Hi Trevor,

You make the polynomial into a square by dividing the second term by 2 and squaring it.  22 divided by 2 is 11. And 11 squared is 121.  The completed square for the polynomial is then Z^2 + 22Z + 121.  Thus C must equal 121 for the polynomial to be a square.  This polynomial is the square of Z + 11 or (z + 11)^2.

To find the c term that completes the square, divide the coefficient on the z term by 2 and then square it




The c term that completes the square is 121