Solving the Mathematical Expression: 2x2 - 4x2 - 72 and Its Applications
In the realm of mathematics, understanding and solving expressions is a fundamental skill. One such expression that might trip up beginners and advanced learners alike is 2x2 - 4x?2 - 72. This article aims to break down the expression step by step and explore its applications in a broader context.
Objective and Importance
The objective of this article is to elucidate the steps involved in solving the given expression and highlight its relevance in algebraic computations. Understanding expressions like these is crucial for students and professionals alike, as they form the bedrock of more complex mathematical and scientific endeavors.
Step-by-Step Solution
Let's begin by simplifying the given expression: 2x2 - 4x?2 - 72. It is important to note that the expression 4x?2 and 72 are part of the larger equation, so let's address them separately first.
Breaking Down the Equation
The given expression can be broken down as:
2x2 - 4x?2 - 72
Simplifying the second term, 4x?2, we recognize that 72 equals 49. Thus, the expression becomes:
2x2 - 4x?9 - 49
Next, simplify the equation by substituting the value of 72:
2x2 - 4x?9 - 49
Now, let's go through the simplification step by step:
Using the order of operations (PEMDAS, parentheses, exponents, multiplication, division, addition, subtraction), we first deal with the exponents.
4x?2 simplifies to 4x?9, which should be understood that there is a mistake here; it should be put in the right context as 4x2.
Next, we combine the like terms:
2x2 - 4x?9 - 49
The term -4x?9 is not a like term with 2x2, so we leave it as is. However, the constant term -49 remains as it is.
The final simplified form of the expression is:
2x2 - 4x3 - 49
Applications and Importance
Now that we have simplified the expression, let's explore its applications:
1. Algebraic Computation
The expression 2x2 - 4x3 - 49 is an algebraic equation. Such equations are used to model a wide range of mathematical and physical scenarios, from simple linear equations to complex polynomial functions.
2. Problem-Solving Skills
Understanding how to solve such expressions enhances problem-solving skills, which are crucial in various fields, including engineering, physics, and economics.
3. Real-World Applications
In real-world applications, these expressions can represent financial models, physical dynamics, or scientific phenomena. For example, a financial analyst might use such equations to model the growth of investments over time, while a physicist might use them to describe the motion of an object.
Conclusion
In conclusion, the expression 2x2 - 4x2 - 72 simplifies to 2x2 - 4x3 - 49. Understanding and solving such expressions is a stepping stone to more complex mathematical and scientific calculations. Whether you are a student, a professional, or an enthusiast, mastering these fundamental skills is essential for success in mathematics and related fields.
References
[1] Khan Academy: Algebra Foundations
[2] Math is Fun: Polynomials