SOLUTION: please help me solve this equation, I have to complete the square to solve the equation below x^2+x=11/4

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Question 1060489: please help me solve this equation, I have to complete the square to solve the equation below

x^2+x=11/4
Found 2 solutions by Fombitz, Edwin McCravy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Take 1/2 the x coefficient, square it and add it to both sides.
x%5E2%2Bx=11%2F4
x%5E2%2Bx%2B%281%2F2%29%5E2=11%2F4%2B%281%2F2%29%5E2
%28x%2B1%2F2%29%5E2=11%2F4%2B1%2F4
%28x%2B1%2F2%29%5E2=12%2F4
%28x%2B1%2F2%29%5E2=3
x%2B1%2F2=0+%2B-+sqrt%283%29
x=-1%2F2+%2B-+sqrt%283%29

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2Bx%22%22=%22%2211%2F4

x%5E2%2B1x%22%22=%22%2211%2F4

The coefficient of x is 1.
Multiply it by 1%2F2.   1%2Aexpr%281%2F2%29%22%22=%22%221%2F2
Square what you get.        %281%2F2%29%5E2%22%22=%22%221%2F4
Add that to both sides of the equation.

x%5E2%2B1x%2B1%2F4%22%22=%22%2211%2F4%2B1%2F4

The left side now factors as %28x%2B1%2F2%29%28x%2B1%2F2%29 which we write
simply as %28x%2B1%2F2%29%5E2, and combine the terms on the right.

%28x%2B1%2F2%29%5E2%22%22=%22%2212%2F4

Since 12%2F4=3,

%28x%2B1%2F2%29%5E2%22%22=%22%223

We take square roots of both sides, remembering the ± on the right:

x%2B1%2F2%22%22=%22%22%22%22+%2B-+sqrt%283%29

Now we get two answers, one using the + sign and one using the - sign:

x%2B1%2F2%22%22=%22%22%22%22+%2B+sqrt%283%29, x%2B1%2F2%22%22=%22%22%22%22+-+sqrt%283%29 

x%22%22=%22%22-1%2F2+%2B+sqrt%283%29, x%22%22=%22%22-1%2F2+-+sqrt%283%29

Edwin