SOLUTION: Solve by completing the square: x2 + 6x + 2 = 0

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Question 90222: Solve by completing the square:
x2 + 6x + 2 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x%2B2 Start with the given equation


x%5E2%2B6x=-2 Subtract 2 from both sides

1%28x%5E2%2B6x%29=-2 Factor out 1



Take half of 6 to get 3 (ie 6%2F2=3)
Now square 3 to get 9 (ie 3%5E2=9)



1%28x%5E2%2B6x%2B9%29=-2 Add this result (9) inside the parenthesis

1%28x%5E2%2B6x%2B9%29=-2%2B9%281%29 Add 9(1) to the other side (remember we factored out a 1)

Now the left side is a complete square

1%28x%2B3%29%5E2=-2%2B9%281%29 Factor the left side

1%28x%2B3%29%5E2=7 Multiply and combine like terms on the right side

x%2B3=0%2B-sqrt%287%29 Take the square root of both sides

x=-3%2B-sqrt%287%29 Subtract 3 from both sides

So the expression breaks down to
x=-3%2Bsqrt%287%29 or x=-3-sqrt%287%29


So our answer is approximately
x=-0.354248688935409 or x=-5.64575131106459

Here is visual proof

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2%2B6x%2B2%29+ graph of y=x%5E2%2B6x%2B2


When we use the root finder feature on a calculator, we would find that the x-intercepts are x=-0.354248688935409 and x=-5.64575131106459, so this verifies our answer.