Question

Explain the process of completing the square in your own words. Provide an example quadratic equation and solve it using the completing the square process. Explain each step in detail.

Answer 1

Completing the square is a technique for solving quadratic equations by converting them into a perfect square trinomial. An example equation is x^2 + 6x + 5, which when solved by completing the square, yields solutions x = -1 and x = -5.

Step-by-step explanation:

Completing the square is a method used to solve quadratic equations. It involves rewriting the equation in the form of a perfect square trinomial, making it easier to solve. Let's consider the example equation x^2 + 6x + 5 = 0.

Steps for Completing the Square

First, move the constant term to the other side: x^2 + 6x = -5.

Take half of the coefficient of x, which is 3, square it (9), and add it to both sides to form a perfect square on the left: x^2 + 6x + 9 = 4.

The left side is now a perfect square: (x + 3)^2 = 4.

Take the square root of both sides: x + 3 = ±√4, which simplifies to x + 3 = ± 2.

Finally, solve for x: x = -3 ± 2, giving the solutions x = -1 and x = -5.

By completing the square, we've solved the quadratic equation with precision.