Problem 75 Evaluate. $$ -x^{2}-5 x, \te... [FREE SOLUTION]

Chapter 1: Problem 75

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

Short Answer

Expert verified

-9 + 15 = 6

Step by step solution

Substitute the value of x

First, replace the given variable in the expression with the given value. Here, substitute $ x = -3 $ into the expression $ -x^{2} - 5x $.

Calculate $ x^{2} $

Find the value of $ x^{2} $ by squaring $ x $. Since $ x = -3 $, $ x^{2} = (-3)^{2} = 9 $.

Calculate $ -x^{2} $

Now apply the negative sign to $ x^{2} $. Therefore, $ -x^{2} = -9 $.

Calculate $ -5x $

Next, substitute $ x = -3 $ into $ -5x $. This gives $ -5(-3) = 15 $.

Add the results

Finally, add the results from Step 3 and Step 4 together. So, $ -9 + 15 = 6 $.

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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 technique in algebra. It involves replacing the variable in an expression with its given value. In our example, we start by substituting the value of $ x = -3 $ into the expression $ -x^{2} - 5x $. This makes our expression easier to work with since we now have numbers instead of variables. Think of it as 'plugging in' the given number wherever you see the variable.

Squaring a Number

Squaring a number means multiplying the number by itself. When we substituted $ x = -3 $ in our expression, we needed to find $ x^2 $. Since $ x = -3 $:
So, $ (-3)^2 = 9 $. It is essential to remember that squaring a negative number results in a positive number. This is because multiplying two negative numbers gives a positive result. Hence, $ (-3) \times (-3) = 9 $.

Negative Signs in Algebra

Negative signs can sometimes be confusing, but with practice, they become more manageable. In our problem, we had to calculate $ -x^2 $. After squaring, we found that $ x^2 = 9 $. Now, consider the negative sign in front:
$ -x^2 $ becomes $ -9 $. Another place we encountered negative signs was in the term $ -5x $. Here, substituting $ x = -3 $, we calculated:
$ -5(-3) = 15 $. This step reinforces the rule that the product of two negative numbers is positive.

Simplifying Expressions

Simplifying expressions means breaking them down into their simplest form. In the final step of the exercise, we had two simplified results: $ -9 $ and $ 15 $. By adding these two numbers together:
$ -9 + 15 = 6 $. Simplification helps in reducing complex expressions to simpler, more manageable forms. Always perform arithmetic operations, like addition or subtraction, carefully to avoid mistakes.

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91影视

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

Short Answer

Step by step solution

Substitute the value of x

Calculate \( x^{2} \)

Calculate \( -x^{2} \)

Calculate \( -5x \)

Add the results

Key Concepts

Substitution Method

Squaring a Number

Negative Signs in Algebra

Simplifying Expressions

One App. One Place for Learning.

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