SOLUTION: SOLVE BY COMPLETING THE SQUARE M^2 - (1/2)M = (7/2)

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Question 204240: SOLVE BY COMPLETING THE SQUARE
M^2 - (1/2)M = (7/2)
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
SOLVE BY COMPLETING THE SQUARE
M%5E2+-+%281%2F2%29+M+=+7%2F2
:
M%5E2+-+%281%2F2%29M+ ___ = 7%2F2
divide the coefficient of m by 2 and square it, add to both sides
M%5E2+-+%281%2F2%29M+%2B+1%2F16 = 7%2F2+%2B+1%2F16
:
M%5E2+-+%281%2F2%29M+%2B+1%2F16 = 56%2F16+%2B+1%2F16
:
M%5E2+-+%281%2F2%29M+%2B+1%2F16 = 57%2F16
:
%28M+-+1%2F4%29%5E2 = 57%2F16
Find the square root of both sides:
M+-+1%2F4 = +/-sqrt%2857%2F16%29
:
M+-+1%2F4 = +/-%281%2F4%29sqrt%2857%29
:
M = 1%2F4+%2B-+%281%2F4%29sqrt%2857%29
we can write the two solutions:
M = %281+%2B+sqrt%2857%29%29%2F4
and
M = %281+-+sqrt%2857%29%29%2F4