To solve the equation $x^2 + 2x - 3 = 0$ by completing the square, follow these steps:

Step 1: Move the constant term to the other side

Rewrite the equation to isolate the $x$-terms: $x^2 + 2x = 3$

Step 2: Complete the square

To complete the square, take half of the coefficient of $x$, square it, and add it to both sides.

1. The coefficient of $x$ is 2. Half of this is $1$, and squaring it gives $1^2 = 1$.
2. Add 1 to both sides: $x^2 + 2x + 1 = 3 + 1$ This simplifies to: $(x + 1)^2 = 4$

Step 3: Take the square root of both sides

Now, take the square root of both sides to solve for $x$: $x + 1 = \pm 2$

Step 4: Solve for $x$

Subtract 1 from both sides:

1. $x = -1 + 2 = 1$
2. $x = -1 - 2 = -3$

Final Answer

The solutions are: $x = 1 \quad \text{or} \quad x = -3$

Would you like a deeper explanation or have any questions?

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1. How does completing the square help solve quadratic equations in other contexts?
2. Can completing the square be used for equations with coefficients other than 1 for $x^2$?
3. How do we determine whether to use completing the square or the quadratic formula?
4. What are real-life applications of completing the square?
5. How does completing the square relate to the formula for the vertex of a parabola?

Tip: Completing the square is also useful for rewriting quadratic functions in vertex form, which reveals the maximum or minimum point of the parabola.