What Is The Value Of $2c^2 + 3$ When $c = 5$?
Introduction
In mathematics, the value of an expression can be determined by substituting the given values into the expression. In this case, we are given the expression $2c^2 + 3$ and the value of $c = 5$. Our goal is to find the value of the expression when $c = 5$. This problem involves basic algebra and substitution.
Understanding the Expression
The given expression is $2c^2 + 3$. This is a quadratic expression, which means it has a squared variable ($c^2$) and a constant term ($3$). The coefficient of the squared term is $2$, which means that the expression will be multiplied by $2$ when we substitute the value of $c$.
Substituting the Value of $c$
To find the value of the expression when $c = 5$, we need to substitute $5$ for $c$ in the expression. This means that we will replace every instance of $c$ with $5$.
Calculating the Value
Now that we have substituted the value of $c$, we can calculate the value of the expression.
Conclusion
In this problem, we were given the expression $2c^2 + 3$ and the value of $c = 5$. We substituted the value of $c$ into the expression and calculated the value of the expression. The final answer is $53$.
Step-by-Step Solution
Here is a step-by-step solution to the problem:
- Understand the expression: The given expression is $2c^2 + 3$.
- Substitute the value of $c$: Replace every instance of $c$ with $5$.
- Calculate the value: $2(5)^2 + 3$, $2(25) + 3$, $50 + 3$, $53$.
- Final answer: The final answer is $53$.
Frequently Asked Questions
- What is the value of $2c^2 + 3$ when $c = 5$?
- The final answer is $53$.
- How do I substitute the value of $c$ into the expression?
- Replace every instance of $c$ with the given value.
- What is the coefficient of the squared term in the expression?
- The coefficient of the squared term is $2$.
Related Problems
- What is the value of $3c^2 + 2$ when $c = 4$?
- To solve this problem, substitute $4$ for $c$ in the expression and calculate the value.
- What is the value of $c^2 + 1$ when $c = 3$?
- To solve this problem, substitute $3$ for $c$ in the expression and calculate the value.
Conclusion
In this article, we have discussed how to find the value of a quadratic expression when given the value of the variable. We have used the expression $2c^2 + 3$ and the value of $c = 5$ as an example. We have also provided a step-by-step solution to the problem and answered some frequently asked questions.
Introduction
Quadratic expressions are a fundamental concept in algebra, and understanding how to work with them is crucial for solving a wide range of mathematical problems. In this article, we will answer some frequently asked questions about quadratic expressions, including how to substitute values into an expression, how to calculate the value of an expression, and more.
Q&A
Q: What is a quadratic expression?
A: A quadratic expression is an algebraic expression that contains a squared variable (such as $c^2$) and a constant term. It is typically written in the form $ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.
Q: How do I substitute a value into a quadratic expression?
A: To substitute a value into a quadratic expression, simply replace the variable (such as $c$) with the given value. For example, if we have the expression $2c^2 + 3$ and we want to substitute $c = 5$, we would replace every instance of $c$ with $5$.
Q: How do I calculate the value of a quadratic expression?
A: To calculate the value of a quadratic expression, follow these steps:
- Substitute the given value into the expression.
- Simplify the expression by combining like terms.
- Evaluate the expression to find the final value.
Q: What is the difference between a quadratic expression and a linear expression?
A: A quadratic expression contains a squared variable (such as $c^2$), while a linear expression does not contain a squared variable. For example, $2c^2 + 3$ is a quadratic expression, while $2c + 3$ is a linear expression.
Q: Can I simplify a quadratic expression?
A: Yes, you can simplify a quadratic expression by combining like terms. For example, if we have the expression $2c^2 + 3c + 2$, we can simplify it by combining the like terms: $2c^2 + 3c + 2 = 2c^2 + 2c + c + 2 = 2c(c + 1) + 2(c + 1) = (2c + 2)(c + 1)$.
Q: How do I factor a quadratic expression?
A: To factor a quadratic expression, look for two numbers whose product is the constant term and whose sum is the coefficient of the squared term. For example, if we have the expression $c^2 + 5c + 6$, we can factor it by finding the two numbers whose product is $6$ and whose sum is $5$: $c^2 + 5c + 6 = (c + 3)(c + 2)$.
Q: What is the value of $2c^2 + 3$ when $c = 5$?
A: To find the value of the expression when $c = 5$, substitute $5$ for $c$ in the expression and calculate the value: $2(5)^2 + 3 = 2(25) + 3 = 50 + 3 = 53$.
Q: What is the value of $3c^2 + 2$ when $c = 4$?
A: To find the value of the expression when $c = 4$, substitute $4$ for $c$ in the expression and calculate the value: $3(4)^2 + 2 = 3(16) + 2 = 48 + 2 = 50$.
Q: What is the value of $c^2 + 1$ when $c = 3$?
A: To find the value of the expression when $c = 3$, substitute $3$ for $c$ in the expression and calculate the value: $(3)^2 + 1 = 9 + 1 = 10$.
Conclusion
In this article, we have answered some frequently asked questions about quadratic expressions, including how to substitute values into an expression, how to calculate the value of an expression, and more. We hope that this article has been helpful in clarifying some of the concepts related to quadratic expressions.