Evaluate $x^2+14$ For $x=-5$.A) -39 B) 39 C) 11 D) -11

Introduction

Evaluating algebraic expressions is a fundamental concept in mathematics, and it is essential to understand how to substitute values into expressions to find their results. In this article, we will evaluate the expression $x^2+14$ for $x=-5$. This involves substituting the value of $x$ into the expression and simplifying the result.

Understanding the Expression

The given expression is $x^2+14$. This is a quadratic expression, which means it contains a squared variable ($x^2$) and a constant term ($14$). To evaluate this expression, we need to substitute the value of $x$ into the expression and simplify the result.

Substituting the Value of $x$

To evaluate the expression $x^2+14$ for $x=-5$, we need to substitute $x=-5$ into the expression. This means we replace every instance of $x$ with $-5$.

Evaluating the Expression

Now that we have substituted the value of $x$ into the expression, we can simplify the result. The expression becomes:

$(-5)^2+14$

To evaluate this expression, we need to follow the order of operations (PEMDAS):

1. Evaluate the exponent: $(-5)^2 = 25$
2. Add the constant term: $25+14 = 39$

Therefore, the value of the expression $x^2+14$ for $x=-5$ is $39$.

Conclusion

Evaluating algebraic expressions is a crucial skill in mathematics, and it is essential to understand how to substitute values into expressions to find their results. In this article, we evaluated the expression $x^2+14$ for $x=-5$ and found that the result is $39$. This demonstrates the importance of following the order of operations and simplifying expressions to find their values.

Frequently Asked Questions

• Q: What is the value of $x^2+14$ for $x=-5$? A: The value of $x^2+14$ for $x=-5$ is $39$.
• Q: How do I evaluate an algebraic expression? A: To evaluate an algebraic expression, you need to substitute the value of the variable into the expression and simplify the result.
• Q: What is the order of operations? A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Final Answer

The final answer is $\boxed{39}$.

Introduction

Evaluating algebraic expressions is a fundamental concept in mathematics, and it is essential to understand how to substitute values into expressions to find their results. In this article, we will provide a Q&A guide on evaluating algebraic expressions, including common mistakes to avoid and tips for simplifying expressions.

Q&A Guide

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. Examples of algebraic expressions include $x^2+3x-4$ and $2x^3-5x^2+1$.

Q: How do I evaluate an algebraic expression?

A: To evaluate an algebraic expression, you need to substitute the value of the variable into the expression and simplify the result. For example, to evaluate the expression $x^2+14$ for $x=-5$, you would substitute $x=-5$ into the expression and simplify the result.

Q: What is the order of operations?

A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. This means that you should evaluate expressions inside parentheses first, followed by exponents, then multiplication and division, and finally addition and subtraction.

Q: What is the difference between an expression and an equation?

A: An expression is a mathematical statement that contains variables, constants, and mathematical operations, but does not contain an equal sign. An equation is a mathematical statement that contains an equal sign and is used to solve for a variable. For example, $x^2+3x-4$ is an expression, while $x^2+3x-4=0$ is an equation.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, you need to combine like terms and eliminate any unnecessary parentheses or brackets. For example, the expression $2x^2+3x-4+2x^2$ can be simplified by combining the like terms $2x^2$ and $2x^2$ to get $4x^2+3x-4$.

Q: What are some common mistakes to avoid when evaluating algebraic expressions?

A: Some common mistakes to avoid when evaluating algebraic expressions include:

• Forgetting to substitute the value of the variable into the expression
• Not following the order of operations
• Not combining like terms
• Not eliminating unnecessary parentheses or brackets

Q: How do I evaluate an expression with multiple variables?

A: To evaluate an expression with multiple variables, you need to substitute the values of all the variables into the expression and simplify the result. For example, to evaluate the expression $x^2+3y-4$ for $x=2$ and $y=3$, you would substitute $x=2$ and $y=3$ into the expression and simplify the result.

Q: What is the difference between a variable and a constant?

A: A variable is a symbol that represents a value that can change, while a constant is a value that does not change. For example, $x$ is a variable, while $4$ is a constant.

Q: How do I evaluate an expression with a negative exponent?

A: To evaluate an expression with a negative exponent, you need to rewrite the expression with a positive exponent and then simplify the result. For example, the expression $x^{-2}$ can be rewritten as $\frac{1}{x^2}$.

Conclusion

Evaluating algebraic expressions is a crucial skill in mathematics, and it is essential to understand how to substitute values into expressions to find their results. By following the order of operations and simplifying expressions, you can evaluate algebraic expressions with confidence. Remember to avoid common mistakes, such as forgetting to substitute the value of the variable into the expression and not following the order of operations.

Frequently Asked Questions

• Q: What is an algebraic expression? A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations.
• Q: How do I evaluate an algebraic expression? A: To evaluate an algebraic expression, you need to substitute the value of the variable into the expression and simplify the result.
• Q: What is the order of operations? A: The order of operations is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Final Answer

The final answer is $\boxed{39}$.