SOLUTION: solve equation by completing the square x^2 + 10x + 13 = 0

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Question 133273: solve equation by completing the square
x^2 + 10x + 13 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=1+x%5E2%2B10+x%2B13 Start with the given equation


y-13=1+x%5E2%2B10+x Subtract 13 from both sides


y-13=1%28x%5E2%2B10x%29 Factor out the leading coefficient 1


Take half of the x coefficient 10 to get 5 (ie %281%2F2%29%2810%29=5).

Now square 5 to get 25 (ie %285%29%5E2=%285%29%285%29=25)




y-13=1%28x%5E2%2B10x%2B25-25%29 Now add and subtract this value inside the parenthesis. Doing both the addition and subtraction of 25 does not change the equation



y-13=1%28%28x%2B5%29%5E2-25%29 Now factor x%5E2%2B10x%2B25 to get %28x%2B5%29%5E2


y-13=1%28x%2B5%29%5E2-1%2825%29 Distribute


y-13=1%28x%2B5%29%5E2-25 Multiply


y=1%28x%2B5%29%5E2-25%2B13 Now add 13 to both sides to isolate y


y=1%28x%2B5%29%5E2-12 Combine like terms



1%28x%2B5%29%5E2-12=0 Now to solve for x, let y=0


1%28x%2B5%29%5E2=%2B12 Add 12 to both sides


%28x%2B5%29%5E2=%2812%29%2F%281%29 Divide both sides by 1


%28x%2B5%29%5E2=12 Reduce


Take the square root of both sides


Subtract 5 from both sides




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Answer:


So the solutions are

x=-5+%2B+sqrt%2812%29 or x=-5+-+sqrt%2812%29