SOLUTION: solve the following equation by completeing the square x2+3x=5

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Question 134326This question is from textbook beginning algebra
: solve the following equation by completeing the square
x2+3x=5 This question is from textbook beginning algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2B3+x=5 Start with the given equation


Take half of the x coefficient 3 to get 3%2F2 (ie %281%2F2%29%283%29=3%2F2).

Now square 3%2F2 to get 9%2F4 (ie %283%2F2%29%5E2=%283%2F2%29%283%2F2%29=9%2F4)




x%5E2%2B3x%2B9%2F4-9%2F4=5 Now add and subtract this value on the left side. Doing both the addition and subtraction of 9%2F4 does not change the equation



%28x%2B3%2F2%29%5E2-9%2F4=5 Now factor x%5E2%2B3x%2B9%2F4 to get %28x%2B3%2F2%29%5E2


%28x%2B3%2F2%29%5E2=9%2F4%2B5 Add 9%2F4 to both sides


%28x%2B3%2F2%29%5E2=29%2F4 Combine like terms



Take the square root of both sides


Simplify

Subtract 3%2F2 from both sides

Combine the fractions



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Answer:


So our solutions are

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