Expressions are essential building elements in algebra that help you model and comprehend a variety of mathematical ideas. One such formula that frequently stumps pupils is “58. 2x ^ 2 – 9x ^ 2; 5 – 3x + y + 6” This post will look at this claim, break it down, simplify each part, and then offer a methodical fix. By the conclusion, you will have a solid understanding of the phrase and its applications.
An Overview of the Expression: 58. 2x ^ 2 – 9x ^ 2; 5 – 3x + y + 6
Let’s take a time to comprehend the structure of the provided phrase before we begin to simplify it. The Equation consist of two components, with a semicolon between them. “2x^2 – 9x^2” is the first portion, while “5 – 3x + y + 6” is the second.
Dividing the Expression into its Steps
- 2x^2 – 9x^2
We will divide the first component of the statement, “2x^2 – 9x^2,” in this section. There are two terms in the expression: “-2x^2” and “-9x^2.” Variables (x) raised to the power of two are present in both phrases.
- 5 – 3x + y + 6
We now address the second portion of the formula, which reads, “5 – 3x + y + 6.” There are more words in this section as well: “5,” “-3x,” “y,” and “6.” Every term has variables and a coefficient.
Breaking Down Each Word into Its Simplex
- Simplifying 2x^2 – 9x^2
We must merge the similar phrases in order to simplify the first section. The same variable (x), raised to the power of two, appears in both phrases. The result of adding “-2x^2” and “-9x^2” is “-7x^2.”
- Simplifying 5 – 3x + y + 6
We’ll simplify the expression’s second portion in this section. We leave the terms alone as there are no similar terms to combine.
Also Read about: 4x ^ 2 – 5x – 12 = 0
Joining the Breakdown Parts
Now that both sections have been made simpler, we can put them back together. The formula “-7x^2; 5 – 3x + y + 6” is the simplified version.
Calculating the Expression
In order to solve the expression, we must give the variable (x) a particular value and then evaluate the expression using that value. Using an example will help:
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
Uses of Quadratic Equations
Numerous important applications of the quadratic equation may be found in a wide range of professions and disciplines. Among them are, to name a few:
- In Physics
It assists with the solving of any issues related to projectile motions, which are basically the moving or repositioning of any object.
- In Engineering and Design
It is helpful for researching electrical circuits, signal processing, and load distribution in structural analysis and for making critical judgments in these areas. It is consequently very useful for engineers working in their respective fields.
- In Economics and Finance
It makes it easier to apply techniques for calculating return on investment and to modify financial systems in the case of a complex economic structure.
In conclusion
Even though the algebraic formula “58. 2x ^ 2 – 9x ^ 2; 5 – 3x + y + 6” looks complicated at first, its structure may be better understood by dissecting it, making each component simpler, and then putting them back together. Additionally, figuring out the expression for particular variable values enables us to assess the variable’s numerical value in various contexts. Algebraic expressions are an essential subject to understand in mathematics because of their practical significance.
