SOLUTION: Solve by completing the square: x^2 + 6x + 4 = 0

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Question 167787: Solve by completing the square:
x^2 + 6x + 4 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2%2B6x%2B4 Start with the left side of the given equation.


Take half of the x coefficient 6 to get 3. In other words, %281%2F2%29%286%29=3.


Now square 3 to get 9. In other words, %283%29%5E2=%283%29%283%29=9


x%5E2%2B6x%2Bhighlight%289-9%29%2B4 Now add and subtract 9. Make sure to place this after the "x" term. Notice how 9-9=0. So the expression is not changed.


%28x%5E2%2B6x%2B9%29-9%2B4 Group the first three terms.


%28x%2B3%29%5E2-9%2B4 Factor x%5E2%2B6x%2B9 to get %28x%2B3%29%5E2.


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


So after completing the square, x%5E2%2B6x%2B4 transforms to %28x%2B3%29%5E2-5. So x%5E2%2B6x%2B4=%28x%2B3%29%5E2-5.


So x%5E2%2B6x%2B4=0 is equivalent to %28x%2B3%29%5E2-5=0.



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


%28x%2B3%29%5E2=0%2B5Add 5 to both sides.


%28x%2B3%29%5E2=5 Combine like terms.


x%2B3=0%2B-sqrt%285%29 Take the square root of both sides.


x%2B3=sqrt%285%29 or x%2B3=-sqrt%285%29 Break up the "plus/minus" to form two equations.


x=-3%2Bsqrt%285%29 or x=-3-sqrt%285%29 Subtract 3 from both sides.


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Answer:


So the solutions are x=-3%2Bsqrt%285%29 or x=-3-sqrt%285%29.