Question

How can you utilize the 'complete the square' method in algebraic equations? Explain the steps, including dividing the coefficient of the x term by 2, squaring it, and adding it to both sides. For example, when dealing with the expression (b/2a)², how does this process work and what does it achieve?

Answer 1

The 'complete the square' method is used to solve quadratic equations by rearranging the equation so that one side is a perfect square trinomial. The steps involve dividing the coefficient of the x term by 2, squaring it, and adding it to both sides of the equation. This process can be used on expressions such as (b/2a)².

Step-by-step explanation:

The 'complete the square' method is used to solve quadratic equations by rearranging the equation so that one side is a perfect square trinomial. Here are the steps:

1. Divide the coefficient of the x term by 2.
2. Square the result from step 1.
3. Add the squared result to both sides of the equation.
4. Factor the perfect square trinomial on one side of the equation, and simplify the other side.
5. Solve for x by taking the square root of both sides (if necessary) and simplifying.

For example, when dealing with the expression (b/2a)², this process works by dividing b by 2a, squaring the result, and then adding it to both sides of the equation to complete the square.