SOLUTION: solve equation by completing the square x^2 + x - 5 = 0

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Question 134476: solve equation by completing the square
x^2 + x - 5 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

y=x%5E2%2Bx-5 Start with the given equation


y%2B5=x%5E2%2Bx Add 5 to both sides



Take half of the x coefficient 1 to get 1%2F2 (ie %281%2F2%29%281%29=1%2F2).

Now square 1%2F2 to get 1%2F4 (ie %281%2F2%29%5E2=%281%2F2%29%281%2F2%29=1%2F4)




y%2B5=x%5E2%2Bx%2B1%2F4-1%2F4 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 1%2F4 does not change the equation



y%2B5=%28x%2B1%2F2%29%5E2-1%2F4 Now factor x%5E2%2B1x%2B1%2F4 to get %28x%2B1%2F2%29%5E2


y%2B5=%28x%2B1%2F2%29%5E2-1%2F4 Multiply


y=%28x%2B1%2F2%29%5E2-1%2F4-5 Now add %2B5 to both sides to isolate y


y=%28x%2B1%2F2%29%5E2-21%2F4 Combine like terms



%28x%2B1%2F2%29%5E2-21%2F4=0 Now to solve for x, let y=0


%28x%2B1%2F2%29%5E2=%2B21%2F4 Add 21%2F4 to both sides


Take the square root of both sides


Simplify


Subtract 1%2F2 from both sides


Combine the fractions


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Answer:

So our solutions are or