Problem 57 Evaluate. $$ -3-x^{2}+12 x, ... [FREE SOLUTION]

Chapter 15: Problem 57

Evaluate. $$ -3-x^{2}+12 x, \text { for } x=5 $$

Short Answer

Expert verified

-3-5^{2}+12*5=32

Step by step solution

Substitute the Value of x

First, replace every occurrence of the variable x in the expression with the given value, which is 5. The expression becomes -3-(5)^{2}+12(5).

Calculate the Exponent

Next, calculate the exponent term (5)^{2} = 25. So, the expression now is: -3 - 25 + 12(5).

Multiply the Terms

Then, multiply 12 by 5. 12(5) = 60. So, the expression becomes: -3 - 25 + 60.

Perform Addition and Subtraction

Finally, perform the addition and subtraction from left to right. -3 - 25 = -28 Now, -28 + 60 = 32.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Substitution

Substitution is a key concept in evaluating mathematical expressions where variables are involved.
Here, you replace the variable with a given value.
In our exercise, the value of $x$ is given as 5.
So, in the expression $-3 - x^{2} + 12x$, replace every $x$ with 5.
It becomes $-3 - (5)^{2} + 12(5)$.
This step helps transition the expression from a variable-dependent form to a numerical form.

Exponents

Exponents involve raising a number to a specified power.
In the expression, $5^{2}$ means multiplying 5 by itself.
Therefore, $(5)^{2} = 25$.
After substitution, we calculate the exponent, transforming $-3 - (5)^{2} + 12(5)$ to $-3 - 25 + 12(5)$.
This simplifies the next steps in evaluating the expression.

Order of Operations

The order of operations is crucial for evaluating expressions correctly.
The commonly followed rule is PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
This rule ensures that calculations are performed in a consistent way.
In our problem, after handling the exponent, next comes multiplication: 12 times 5.
The expression now simplifies to $-3 - 25 + 60$.

Arithmetic Operations

Arithmetic operations are fundamental math operations like addition, subtraction, multiplication, and division.
After dealing with substitution, exponents, and multiplication, what remains is to perform addition and subtraction.
Starting from the left, we first perform the subtraction: $-3 - 25 = -28$.
Next, we add 60 to $-28$, resulting in $-28 + 60 = 32$.
Hence, the final evaluated value of the expression $-3 - x^{2} + 12x$ where $x = 5$ is 32.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Evaluate. $$ -3-x^{2}+12 x, \text { for } x=5 $$

Short Answer

Step by step solution

Substitute the Value of x

Calculate the Exponent

Multiply the Terms

Perform Addition and Subtraction

Key Concepts

Substitution

Exponents

Order of Operations

Arithmetic Operations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Calculus

Probability and Statistics

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.