Solve by Completing the Square x^2+4x+2=0

Problem

x2+4*x+2=0

Solution

1. Isolate the constant term by subtracting 2 from both sides of the equation.

x2+4*x=−2

2. Calculate the value needed to complete the square by taking half of the coefficient of x and squaring it.

4/2=2

2=4

3. Add the value 4 to both sides of the equation to maintain equality.

x2+4*x+4=−2+4

4. Factor the left side as a perfect square trinomial and simplify the right side.

(x+2)2=2

5. Take the square root of both sides, remembering to include both the positive and negative roots.

x+2=±√(,2)

6. Solve for x by subtracting 2 from both sides.

x=−2±√(,2)

Final Answer

x=−2±√(,2)

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