Solve by Completing the Square x^2+2x-3=0

Problem

x2+2*x−3=0

Solution

1. Move the constant term to the right side of the equation by adding 3 to both sides.

x2+2*x=3

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

(2/2)2=1=1

3. Add the value 1 to both sides of the equation to maintain equality.

x2+2*x+1=3+1

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

(x+1)2=4

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

x+1=±√(,4)

x+1=±2

6. Solve for x by subtracting 1 from both sides for both cases.

x=−1+2⇒x=1

x=−1−2⇒x=−3

Final Answer

x=1,−3

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