Solve by Completing the Square x^2-6x-4=0

Problem

x2−6*x−4=0

Solution

1. Isolate the constant term by adding 4 to both sides of the equation.

x2−6*x=4

2. Identify the coefficient of the x term, which is −6

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

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

x2−6*x+9=4+9

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

(x−3)2=13

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

x−3=±√(,13)

7. Solve for x by adding 3 to both sides.

x=3±√(,13)

Final Answer

x=3±√(,13)

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