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

Question 147242: Solve by completing the square:
x^2 + 6x + 1 = 0

Found 2 solutions by psbhowmick, jim_thompson5910:
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

Take half of the x coefficient to get (ie ).

Now square to get (ie )

Now add and subtract this value inside the parenthesis. Notice how . Since we're adding 0, we're not changing the equation.

Now factor to get

Combine like terms

So after completing the square, becomes .

In other words,

So is equivalent to

Start with the given equation.

Add 8 to both sides.

Take the square root of both sides

Subtract 3 from both sides.

or Break up the expression

or Simplify the square root.

So the answers are or

which approximate to or
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