Using completing the square method to solve: X² + 2x - 3

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?

---

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.

Learn how to solve the quadratic equation x² + 2x - 3 using the completing the square method. This step-by-step guide covers essential algebraic techniques suitable for students in Grades 9-10.

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