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Chapter 5: Problem 55

Evaluate each expression for the given replacement value. \(x^{2}\) if \(x\) is \(-5\)

Short Answer

Expert verified
The value of \(x^2\) when \(x\) is \(-5\) is 25.

Step by step solution

01

Understand the Problem

We need to evaluate the expression \(x^2\) for the given value of \(x\), which is \(-5\). This means we will substitute \(-5\) in place of \(x\) in the expression.
02

Substitute the Value of x

Replace \(x\) with \(-5\) in the expression. Thus, \(x^2\) becomes \((-5)^2\).
03

Calculate the Square

Evaluate \((-5)^2\) by multiplying \(-5\) with itself. \((-5) \times (-5) = 25\).
04

State the Result

The result of the expression \(x^2\) when \(x = -5\) is \(25\).

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Key Concepts

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

Substitution Method
The substitution method is a fundamental concept used in evaluating expressions. It involves replacing variables with specific values to simplify or solve expressions. For example, in an expression like \(x^2\), the variable \(x\) can take various values. Substituting a particular value into the expression helps us find specific results.
  • Step-by-Step: Start by identifying the variable and its corresponding value provided in the problem.
  • Substitution: Plug in that value wherever the variable appears in the expression. For instance, if \(x = -5\), then replace \(x\) with \(-5\).
This method is crucial for turning abstract formulas into tangible results, making it easier to solve problems, especially in algebra and calculus.
Squaring Numbers
Squaring a number means multiplying that number by itself. This operation is indicated by the exponent "2". For instance, \(x^2\) means \(x\) multiplied by itself. When working with squares, consider these points:
  • Positive Results: Squaring any real number, whether positive or negative, results in a positive outcome. For example, both \((5)^2\) and \((-5)^2\) lead to \(25\).
  • Visual Understanding: Think of squaring as a way to "build a square" where each side's length equals the number being squared.
Understanding squaring helps in further mathematical operations, such as solving quadratic equations and analyzing geometric shapes.
Negative Numbers
Negative numbers are values less than zero and are typically denoted with a minus sign (\(-\)). They follow specific rules of arithmetic:
  • Multiplication: Multiplying two negative numbers results in a positive number. For example, \((-5) \times (-5) = 25\).
  • Direction: Adding a negative number is like moving left on a number line, while subtracting a negative number involves moving right.
Comprehending negative numbers is essential as they appear frequently in various mathematical contexts, from basic arithmetic to complex algebraic equations.

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Most popular questions from this chapter

Multiply each expression. $$ -3 x y\left(x y^{2}+7 x^{2} y+8\right) $$

Perform the indicated operations. $$(2 x-1)+(10 x-7)$$

See the Concept Checks in this section. $$5 a+6 a$$

Add or subtract as indicated. See Examples 9 through \(13 .\) $$ \left(7 a^{2}-3 b^{2}+10\right)-\left(-2 a^{2}+b^{2}-12\right) $$

Divide If the divisor contains 2 or more terms, use long division. $$ \frac{y^{3}+3 y^{2}+4}{y-2} $$
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