Problem 87 - Algebra 1

Question

Evaluate the expression. x^{2} \text { when } x=-5

Step-by-Step Solution

Answer

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

Step 1: Identify the given value of x

Here, -5 is provided as the substitute for x in the given expression \(x^{2}\).

Step 2: Substitute x value into the expression

Replace x in the equation \(x^{2}\) with -5. The expression now becomes \((-5)^{2}\).

Step 3: Evaluate the expression

Calculate the square of -5 which equals 25.

Key Concepts

Substitution in Algebra

Substitution in algebra is a straightforward process that involves replacing variables with given values to simplify or evaluate expressions. This technique is commonly used when solving equations or functions. For example:

• Start by identifying the variable that needs a value.
• In our exercise, we had an expression with the variable \( x \), and the given value was \(-5\).
• We substitute \( x \) with \(-5\) in the expression \( x^2 \).

Once substitution is done, the expression can be resolved using proper arithmetic. This foundational skill is crucial in algebra as it simplifies the process of dealing with complex expressions and prepares students for more advanced techniques.

Square Calculation

Square calculation is an essential arithmetic process frequently encountered in algebra. It involves multiplying a number by itself. Here's how it works:

• To calculate the square of a number, take the number and multiply it by itself.
• In our case, we had to find \((-5)^2\), meaning we multiplied \(-5\) by itself.
• The calculation \((-5) \times (-5) = 25\), demonstrates that squaring is not affected by the sign of the number.

Squaring numbers is particularly useful in various areas of math, including geometry and physics. It’s vital to understand this operation fully, as it often serves as a basis for more complex operations and functions.

Negative Numbers in Algebra

Handling negative numbers in algebra might seem tricky, but it's a fundamental skill that simplifies over time with practice. With negative numbers:

• When multiplying two negative numbers, the result is positive. This principle was utilized in our exercise with \((-5) \times (-5)\) resulting in \(25\).
• It's essential to keep track of signs to avoid errors, especially with substitution and multiplication tasks.
• Negative signs often represent inverse directions or values in mathematical modeling and equations.

By understanding how to work with negative numbers effectively, students can tackle a wide range of algebraic expressions, equations, and real-life math problems.