9 answers
To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we start by combining like terms.
Combine the \(x^2\) terms: \[ 14x^2 + 0.75x^2 = 14.75x^2 \]
Combine the \(x\) terms: \[ -3x + 2x = -1x \quad \text{or} \quad -x \]
Combine the constant terms: \[ 2.25 - 14 = -11.75 \]
Now, putting it all together, the simplified sum of the polynomials is: \[ 14.75x^2 - x - 11.75 \]
Thus, the final answer is: \[ \boxed{14.75x^2 - x - 11.75} \]
Let's go through the simplification step-by-step again to ensure accuracy.
We need to simplify the expression:
\[ (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \]
Identify and combine like terms:
For the \(x^2\) terms: \[ 14x^2 + 0.75x^2 = 14.75x^2 \]
For the \(x\) terms: \[ -3x + 2x = -1x \quad \text{or} \quad -x \]
For the constant terms: \[ 2.25 - 14 = 2.25 - 14 = -11.75 \]
Combine all results: Collecting these together, we have: \[ 14.75x^2 - x - 11.75 \]
So the simplified sum of the polynomials is indeed: \[ \boxed{14.75x^2 - x - 11.75} \]
If you believe this answer is still incorrect, please specify the issue.
Let's carefully simplify the expression step by step once more to ensure accuracy.
We have:
\[ (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \]
Start with the \(x^2\) terms: \[ 14x^2 + 0.75x^2 = 14.75x^2 \]
Next, combine the \(x\) terms: \[ -3x + 2x = -1x \quad \text{or} \quad -x \]
Now combine the constant terms: \[ 2.25 - 14 = 2.25 - 14 = -11.75 \]
Now, we combine all these results together. The simplified sum of the polynomials is:
\[ 14.75x^2 - x - 11.75 \]
So, filling in the blank, the sum of the polynomials is: \[ \boxed{14.75x^2 - x - 11.75} \]
If you're looking for a different format or if there's a specific type of solution you're expecting, please let me know!
Apologies for the confusion. Let's start fresh with the given polynomial expression and simplify it step by step properly.
We need to simplify the expression:
\[ (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \]
Let's combine the like terms accurately.
Combine the \(x^2\) terms: \[ 14x^2 + 0.75x^2 = 14.75x^2 \]
Combine the \(x\) terms: \[ -3x + 2x = -1x \quad \text{or} \quad -x \]
Combine the constant terms: \[ 2.25 - 14 = 2.25 - 14 = -11.75 \]
Putting it all together gives us:
\[ 14.75x^2 - x - 11.75 \]
Now, the answer you provided, \(x^2 - x + 2\), seems to imply we should have factored or transformed the expression further.
Let's double-check our original polynomial and see if we can find a mistake or misunderstanding:
From \[ (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \]
It seems everything is accurate upon reevaluation but it doesn’t match \(x^2 - x + 2\).
This suggests there might have been a misunderstanding regarding either the initial expression or a mistake in the original assumptions.
If the intent is to work closer toward \(x^2 - x + 2\), could you provide additional context or clarify the expression to be simplified?
I apologize for the confusion and any frustration my previous responses may have caused. Let’s go over the problem one more time carefully to ensure a clear and correct simplification.
We need to simplify:
\[ (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \]
Combine the \(x^2\) terms: \[ 14x^2 + 0.75x^2 = 14.75x^2 \]
Combine the \(x\) terms: \[ -3x + 2x = -1x \quad \text{or} \quad -x \]
Combine the constant terms: \[ 2.25 - 14 = 2.25 - 14 = -11.75 \]
Now we can combine these results into one simplified expression:
\[ 14.75x^2 - x - 11.75 \]
If this still does not appear to meet your expectations, may I ask if there is perhaps a different approach or method you are looking to achieve, such as factoring or finding roots?
If you meant to simplify or adjust the expression to relate it to \(x^2 - x + 2\), that would not follow from the calculations above but might be the result of a different polynomial expression.
Again, I apologize for any errors and confusion. If you could provide any additional details, I’d be happy to help you resolve this. Thank you for your patience!
