Solve by Completing the Square x^2+6x+1=0

Problem

x2+6*x+1=0

Solution

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

x2+6*x=−1

2. Calculate the value needed to complete the square by taking half of the coefficient of x and squaring it: (6/2)2=3=9

(6/2)2=9

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

x2+6*x+9=−1+9

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

(x+3)2=8

5. Take the square root of both sides, remembering to include the plus-minus symbol.

x+3=±√(,8)

6. Simplify the radical √(,8) to 2√(,2)

x+3=±2√(,2)

7. Solve for x by subtracting 3 from both sides.

x=−3±2√(,2)

Final Answer

x=−3±2√(,2)

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