Completing the square is a technique used in algebra to rewrite a quadratic equation in a specific form called vertex form. The vertex form of a quadratic equation is written as:

y = a(x - h)^2 + k

where (h, k) represents the coordinates of the vertex of the parabola.

To complete the square, follow these steps:

Step 1: Start with a quadratic equation in the form y = ax^2 + bx + c.

Step 2: If the coefficient of x^2 (a) is not 1, divide the entire equation by a to make it equal to 1. This step is necessary to simplify the process.

Step 3: Move the constant term (c) to the right side of the equation.

Step 4: Take half of the coefficient of x (b/2) and square it. Add this value to both sides of the equation.

Step 5: Rewrite the equation as a perfect square trinomial on the left side.

Step 6: Factor the perfect square trinomial and simplify if possible.

Step 7: Write the equation in vertex form by grouping the perfect square trinomial and the constant term.

Step 8: Identify the values of h and k from the vertex form equation. The vertex of the parabola is given by (h, k).

Step 9: Use the vertex form equation to graph the parabola or solve any other related problems.

Completing the square is a useful technique in algebra as it allows us to easily find the vertex of a parabola, solve quadratic equations, and graph quadratic functions. It is also used in various applications such as physics, engineering, and economics.