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

Problem

x2+2*x−5=0

Solution

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

x2+2*x=5

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

3. Calculate the value needed to complete the square by taking half of the x coefficient and squaring it: (2/2)2=1=1

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

x2+2*x+1=5+1

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

(x+1)2=6

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

x+1=±√(,6)

7. Solve for x by subtracting 1 from both sides.

x=−1±√(,6)

Final Answer

x=−1±√(,6)

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