Solve by Completing the Square x^2+6x-5=0

Problem

x2+6*x−5=0

Solution

1. Isolate the constant term by adding 5 to both sides of the equation.

x2+6*x=5

2. Calculate the value needed to complete the square by taking half of the coefficient of x which is 6 and squaring it.

(6/2)2=3=9

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

x2+6*x+9=5+9

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

(x+3)2=14

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

x+3=±√(,14)

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

x=−3±√(,14)

Final Answer

x=−3±√(,14)

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