Answer: m^2 - 13m + 42.25 = (m - 6.5)^2
notes:
6.5 = 13/2
42.25 = 169/4
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Explanation:
The coefficient in front of the m is -13. Cut this in half to get -13/2 = -6.5
Then square this result to get (-6.5)^2 = 42.25
We need to add 42.25 to the expression in order to complete the square
This allows us to factor to get m^2 - 13m + 42.25 = (m - 6.5)^2
Note how the equation is in the form
a^2 - 2ab + b^2 = (a-b)^2
where a = m and b = 6.5
