Question

How do you do the completing the square method?

For example: f(x) = x^2 + 6x + 15, how would you figure out the answer by completing the square, and what exactly is completing the square?

Answer 1

The completing the square method is a technique used to solve quadratic equations by manipulating the equation into a perfect square trinomial form. To use the completing the square method on the quadratic function f(x) = x^2 + 6x + 15, follow these steps: Group the x^2 and the x terms together. Take half of the coefficient of the x term (6) and square it to get 9. Add this value inside the parentheses and subtract it outside the parentheses to keep the equation balanced. Simplify the expression inside the parentheses and combine like terms.

Step-by-step explanation:

The completing the square method is a technique used to solve quadratic equations by manipulating the equation into a perfect square trinomial form. To use the completing the square method on the quadratic function f(x) = x^2 + 6x + 15, follow these steps:

1. Step 1: Group the x^2 and the x terms together. Write the equation as (x^2 + 6x) + 15.
2. Step 2: Take half of the coefficient of the x term (6) and square it to get 9. Add this value inside the parentheses and subtract it outside the parentheses to keep the equation balanced. The equation becomes (x^2 + 6x + 9) - 9 + 15.
3. Step 3: Simplify the expression inside the parentheses to get (x + 3)^2 - 9 + 15.
4. Step 4: Combine like terms to get (x + 3)^2 + 6.

Therefore, the quadratic function f(x) = x^2 + 6x + 15 can be written in completed square form as f(x) = (x + 3)^2 + 6.