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Simplify (14x2−3x+2.25)+(0.75x2+2x−14) .(1 point) The sum of the polynomials is .Asked by Honeybeee
Simplify (14x2−3x+2.25)+(0.75x2+2x−14) .(1 point) The sum of the polynomials is .
Answers
Answered by
GPT-4o mini
To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we start by combining like terms.
1. Combine the \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
2. Combine the \(x\) terms:
\[
-3x + 2x = -1x \quad \text{or} \quad -x
\]
3. 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:
\[
\boxed{14.75x^2 - x - 11.75}
\]
1. Combine the \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
2. Combine the \(x\) terms:
\[
-3x + 2x = -1x \quad \text{or} \quad -x
\]
3. 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:
\[
\boxed{14.75x^2 - x - 11.75}
\]
Answered by
GPT-4o mini
Let's go through the simplification step-by-step again to ensure accuracy.
We need to simplify the expression:
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
1. **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:
\[
2.25 - 14 = 2.25 - 14 = -11.75
\]
2. **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.
We need to simplify the expression:
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
1. **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:
\[
2.25 - 14 = 2.25 - 14 = -11.75
\]
2. **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.
Answered by
GPT-4o mini
Let's carefully simplify the expression step by step once more to ensure accuracy.
We have:
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
1. Start with the \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
2. Next, combine the \(x\) terms:
\[
-3x + 2x = -1x \quad \text{or} \quad -x
\]
3. 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!
We have:
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
1. Start with the \(x^2\) terms:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
2. Next, combine the \(x\) terms:
\[
-3x + 2x = -1x \quad \text{or} \quad -x
\]
3. 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!
Answered by
GPT-4o mini
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.
1. **Combine the \(x^2\) terms:**
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
2. **Combine the \(x\) terms:**
\[
-3x + 2x = -1x \quad \text{or} \quad -x
\]
3. **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
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
1. Check each term:
- \(14x^2 + 0.75x^2\) is correct as \(14.75x^2\).
- \(-3x + 2x\) is correct as \(-1x\).
- \(2.25 - 14\) gives us \(-11.75\).
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?
We need to simplify the expression:
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
Let's combine the like terms accurately.
1. **Combine the \(x^2\) terms:**
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
2. **Combine the \(x\) terms:**
\[
-3x + 2x = -1x \quad \text{or} \quad -x
\]
3. **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
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
1. Check each term:
- \(14x^2 + 0.75x^2\) is correct as \(14.75x^2\).
- \(-3x + 2x\) is correct as \(-1x\).
- \(2.25 - 14\) gives us \(-11.75\).
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?
Answered by
GPT-4o mini
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:
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
### Step 1: Combine Like Terms
1. **Combine the \(x^2\) terms**:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
2. **Combine the \(x\) terms**:
\[
-3x + 2x = -1x \quad \text{or} \quad -x
\]
3. **Combine the constant terms**:
\[
2.25 - 14 = 2.25 - 14 = -11.75
\]
### Step 2: Write it all together
Now we can combine these results into one simplified expression:
\[
14.75x^2 - x - 11.75
\]
### Verification
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!
We need to simplify:
\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]
### Step 1: Combine Like Terms
1. **Combine the \(x^2\) terms**:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]
2. **Combine the \(x\) terms**:
\[
-3x + 2x = -1x \quad \text{or} \quad -x
\]
3. **Combine the constant terms**:
\[
2.25 - 14 = 2.25 - 14 = -11.75
\]
### Step 2: Write it all together
Now we can combine these results into one simplified expression:
\[
14.75x^2 - x - 11.75
\]
### Verification
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!