Solve by Completing the Square x^2-6x-11=0

Problem

x2−6*x−11=0

Solution

1. Move the constant term to the right side of the equation by adding 11 to both sides.

x2−6*x=11

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

(−6)/2=−3

(−3)2=9

3. Add the value 9 to both sides of the equation to maintain equality.

x2−6*x+9=11+9

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

(x−3)2=20

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

x−3=±√(,20)

6. Simplify the radical by factoring out the largest perfect square.

x−3=±2√(,5)

7. Isolate the variable x by adding 3 to both sides.

x=3±2√(,5)

Final Answer

x=3±2√(,5)

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