Simplify x² - 5⅕x²: Subtracting Like Terms with Mixed Numbers

To solve this problem, we'll follow these steps:

• Step 1: Understand the problem components - recognize the operation between two terms involving $x^2$.
• Step 2: Convert mixed numbers to improper fractions if needed and focus on calculating the coefficients.
• Step 3: Perform the subtraction operation.
• Step 4: Write the result as a coefficient of $x^2$.

Now, let's work through each step:

Step 1: The expression involves the subtraction of $(+x^2)$ and $(5\frac{1}{5}x^2)$.

Step 2: Convert $5\frac{1}{5}$ into an improper fraction. This gives us $\frac{26}{5}$.

Step 3: Subtract the coefficients:

• $1 - \frac{26}{5}$ (Recall that $+x^2$ is equivalent to $1x^2$)

Converting 1 into a fraction: $\frac{5}{5}$. Thus, we have:

$\frac{5}{5} - \frac{26}{5} = \frac{5 - 26}{5}$

This simplifies to:

$\frac{-21}{5}$

Step 4: Attach this result to $x^2$. Hence, the expression simplifies to:

$-\frac{21}{5}x^2$

In mixed number form, this is $-4\frac{1}{5}x^2$.

Therefore, the solution to the problem is $-4\frac{1}{5}x^2$.