September 27, 2023 # 58. 2x ^ 2 – 9x ^ 2; 5 – 3x + y + 6: Solving The Quadratic Equation

58. 2x ^ 2 – 9x ^ 2; 5 – 3x + y + 6. In the realm of algebra, expressions serve as fundamental building blocks to model and understand various mathematical concepts. One such expression that often confuses students is “2x^2 – 9x^2; 5 – 3x + y + 6.” In this article, we will delve into this expression, break it down, simplify each part, and finally, solve it step by step. By the end, you’ll have a clear understanding of the expression and its applications.

## Understanding the Expression: 58.2x^2 – 9x^2; 5 – 3x + y + 6

Before we start simplifying the given expression, let’s take a moment to understand its structure. The expression is composed of two parts separated by a semicolon. The first part is “2x^2 – 9x^2,” and the second part is “5 – 3x + y + 6.”

## Breaking Down the Expression

### Part 1: 2x^2 – 9x^2

In this section, we will focus on the first part of the expression, “2x^2 – 9x^2.” The expression consists of two terms: “2x^2” and “-9x^2.” Both terms contain variables (x) raised to the power of 2.

### Part 2: 5 – 3x + y + 6

Now, we move on to the second part of the expression, “5 – 3x + y + 6.” This part also contains multiple terms: “5,” “-3x,” “y,” and “6.” Each term has its coefficient and variables.

## Simplifying Each Part of the Expression

### Part 1: Simplifying 2x^2 – 9x^2

To simplify the first part, we need to combine the like terms. Both terms have the same variable (x) raised to the power of 2. When we combine “2x^2” and “-9x^2,” we get “-7x^2.”

### Part 2: Simplifying 5 – 3x + y + 6

In this section, we’ll simplify the second part of the expression. There are no like terms to combine, so we keep the terms as they are.

## Combining the Simplified Parts

Now that we have simplified both parts, we can combine them back together. The simplified expression is “-7x^2; 5 – 3x + y + 6.”

## Solving the Expression

To solve the expression, we need to provide a specific value for the variable (x) and evaluate the expression based on that value. Let’s take an example:

Suppose we have x = 3; now, let’s find the value of the expression:

-7(3)^2; 5 – 3(3) + y + 6 = -7(9); 5 – 9 + y + 6 = -63; -4 + y + 6 = -63; 2 + y

## Practical Applications of Algebraic Expressions

Algebraic expressions find widespread applications in various fields, including physics, engineering, economics, and computer science. They are used to model and solve real-world problems, analyze data, and make predictions. Understanding algebraic expressions is crucial for advancing in these domains. 