SOLUTION: Solve by completing the square {{{x^2+(7/2) x=7}}}

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Question 130753: Solve by completing the square

x%5E2%2B%287%2F2%29+x=7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B%287%2F2%29+x=7 Start with the given equation



Take half of the x coefficient 7%2F2 to get 7%2F4 (ie %281%2F2%29%287%2F2%29=7%2F4).

Now square 7%2F4 to get 49%2F16 (ie %287%2F4%29%5E2=%287%2F4%29%287%2F4%29=49%2F16)




x%5E2%2B%287%2F2%29x%2B49%2F16-49%2F16=7 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 49%2F16 does not change the equation



%28x%2B7%2F4%29%5E2-49%2F16=7 Factor x%5E2%2B%287%2F2%29x%2B49%2F16 to get %28x%2B7%2F4%29%5E2


%28x%2B7%2F4%29%5E2=7%2B49%2F16 Add 49%2F16 to both sides


%28x%2B7%2F4%29%5E2=161%2F16 Combine the fractions


Take the square root of both sides


Break up the root


Take the square root of 16 to get 4

Subtract 7%2F4 from both sides



Combine the fractions



So the equation breaks down to

or



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Answer:

So our solutions are


or