Solving a Quadratic Equation: A Step-by-Step Guide

When faced with a quadratic equation, it's essential to have a clear understanding of the steps involved in solving it. In this article, we'll delve into the process of solving a quadratic equation using the formula.

To begin with, let's consider a right triangle with sides of lengths 8, 15, and 17 feet. We're looking for the length of one side, which can be represented by the variable x. Since x is a side of the triangle, we know that x = −8 does not satisfy the equation.

Using the formula for the area of a rectangle, we can find the area of the rectangular garden to be 15 square feet. This information will come in handy later in our solution.

In problems involving geometric figures, a sketch can help you visualize the situation. By doing so, we can identify that this is a right triangle with two pairs of consecutive integers as solutions.

If the first integer is n = 11 or n = −12, then the next integer is n + 1. This means that there are two sets of consecutive integers that will work: 11 and 12, and −12 and −11.

To find the product of these consecutive integers, we can set up an equation. Let's say that the first integer is n, and the next integer is n + 1. We know that their product is 132. Therefore, we can write the equation as:

n(n+1) = 132

By rearranging this equation, we can solve for n, which gives us two values: n = 11 and n = −12.

These values represent the first integer in each of the two pairs of consecutive integers that satisfy the equation. Since there are two sets of solutions, we have two values for n that are solutions to this problem.

In conclusion, solving a quadratic equation involves breaking it down into smaller steps and using the formula to find the solution. By following these steps, you can easily solve complex equations like the one presented in this article.

Solving a quadratic equation