SOLUTION: Could someone please show me how to solve by completing the square? x^2+3/2 x=3

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Question 528072: Could someone please show me how to solve by completing the square? x^2+3/2 x=3
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve by completing the square? x%5E2+%2B+3%2F2x = 3
:
x%5E2+%2B+3%2F2x + __ = 3
Find the term that will complete the square. Divide the coefficient of x by 2 and square it, add to both sides
x%5E2+%2B+3%2F2x + 9%2F16 = 3 + 9%2F16
x%5E2+%2B+3%2F2x + 9%2F16 = 48%2F16 + 9%2F16
x%5E2+%2B+3%2F2x + 9%2F16 = 57%2F16
which is
%28x+%2B+3%2F4%29%5E2 = 57%2F16
find the square root of both sides:
%28x+%2B+3%2F4%29 = +/-sqrt%2857%2F16%29
The positive solution
x = -3%2F4 + sqrt%2857%2F16%29
extract the square root of 1/16
x = -3%2F4 + %281%2F4%29sqrt%2857%29
Which is
x = %28-3%2Bsqrt%2857%29%29%2F4
and the negative solution
x = %28-3-sqrt%2857%29%29%2F4