SOLUTION: solve by completing the square: x^2+7/2x=7

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Question 259988: solve by completing the square: x^2+7/2x=7
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+%287%2F2%29x+%2B+__+=+7
Find the value that completes the square %28%281%2F2%29%2A%287%2F2%29%29%5E2 = 49%2F16
Add to both sides
x%5E2+%2B+%287%2F2%29x+%2B+%2849%2F16%29+=+7+%2B+%2849%2F16%29
Add the values on the right
x%5E2+%2B+%287%2F2%29x+%2B+%2849%2F16%29+=+%28112%2F16%29+%2B+%2849%2F16%29
:
x%5E2+%2B+%287%2F2%29x+%2B+%2849%2F16%29+=+%28161%2F16%29
which is
%28x+%2B+%287%2F4%29%29%5E2 = 161%2F16
find the square root of both sides
x+%2B+%287%2F4%29 = +/-sqrt%28161%2F16%29
Subtract 7/4 from both sides, Extract the square root of 1/16
x = -7%2F4 +/-sqrt%28161%29%2F4%29
You could write the two solutions;
x = %28-7+%2B+sqrt%28161%29%29%2F4
and
x = %28-7+-+sqrt%28161%29%29%2F4