SOLUTION: Solve by completing the square: x^2 + 6x + 1 = 0

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Question 147242: Solve by completing the square:
x^2 + 6x + 1 = 0
Found 2 solutions by psbhowmick, jim_thompson5910:
Answer by psbhowmick(878) About Me  (Show Source):
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x%2B1 Start with the given expression


Take half of the x coefficient 6 to get 3 (ie %281%2F2%29%286%29=3).

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




x%5E2%2B6x%2B9-9%2B1 Now add and subtract this value inside the parenthesis. Notice how 9-9=0. Since we're adding 0, we're not changing the equation.



%28x%2B3%29%5E2-9%2B1 Now factor x%5E2%2B6x%2B9 to get %28x%2B3%29%5E2


%28x%2B3%29%5E2-8 Combine like terms


So after completing the square, x%5E2%2B6x%2B1 becomes %28x%2B3%29%5E2-8.


In other words, x%5E2%2B6x%2B1=%28x%2B3%29%5E2-8



So x%5E2%2B6x%2B1=0 is equivalent to %28x%2B3%29%5E2-8=0


%28x%2B3%29%5E2-8=0 Start with the given equation.


%28x%2B3%29%5E2=8 Add 8 to both sides.


x%2B3=0%2B-sqrt%288%29 Take the square root of both sides


x=-3%2B-sqrt%288%29 Subtract 3 from both sides.


x=-3%2Bsqrt%288%29 or x=-3-sqrt%288%29 Break up the expression


x=-3%2B2%2Asqrt%282%29 or x=-3-2%2Asqrt%282%29 Simplify the square root.


So the answers are x=-3%2B2%2Asqrt%282%29 or x=-3-2%2Asqrt%282%29


which approximate to x=-0.172 or x=-5.828