Question

Simplify (14x2−3x+2.25)+(0.75x2+2x−14) .(1 point) .
Answer
no decimal
Answer
turn into fraction
Answered by GPT-4o mini
To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we can combine like terms.

First, let's group the terms by their type:

1. Combine the \(x^2\) terms:
\[
14x^2 + 0.75x^2 = (14 + 0.75)x^2 = 14.75x^2
\]

2. Combine the \(x\) terms:
\[
-3x + 2x = (-3 + 2)x = -1x = -x
\]

3. Combine the constant terms:
\[
2.25 - 14 = 2.25 - 14 = -11.75
\]

Now, putting it all together, the simplified expression is:
\[
\boxed{14.75x^2 - x - 11.75}
\]
Answered by GPT-4o mini
To eliminate decimals from the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we can first convert all numbers to fractions and then simplify.

**Convert decimals to fractions**:
- \(2.25 = \frac{9}{4}\)
- \(0.75 = \frac{3}{4}\)

Now rewrite the expression:

\[
(14x^2 - 3x + \frac{9}{4}) + \left(\frac{3}{4}x^2 + 2x - 14\right)
\]

Next, combine like terms:

1. Combine the \(x^2\) terms:
\[
14x^2 + \frac{3}{4}x^2 = \left(14 + \frac{3}{4}\right)x^2 = \left(\frac{56}{4} + \frac{3}{4}\right)x^2 = \frac{59}{4}x^2
\]

2. Combine the \(x\) terms:
\[
-3x + 2x = (-3 + 2)x = -1x = -x
\]

3. Combine the constant terms:
\[
\frac{9}{4} - 14 = \frac{9}{4} - \frac{56}{4} = \frac{9 - 56}{4} = \frac{-47}{4}
\]

Now, putting it all together, we have:

\[
\frac{59}{4}x^2 - x - \frac{47}{4}
\]

To express it without decimals, you can multiply through by 4 to clear the fractions:

\[
4\left(\frac{59}{4}x^2 - x - \frac{47}{4}\right) = 59x^2 - 4x - 47
\]

So, the expression without decimals is:
\[
\boxed{59x^2 - 4x - 47}
\]
Answered by GPT-4o mini
To turn the expression \( (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \) into an entirely fractional form, we can rewrite the decimal numbers as fractions.

### Step 1: Replace Decimals with Fractions

Replace 2.25 and 0.75 with their fractional equivalents:
- \(2.25 = \frac{9}{4}\)
- \(0.75 = \frac{3}{4}\)

### Step 2: Rewrite the Expression

Now, rewrite the original expression using these fractions:

\[
\left(14x^2 - 3x + \frac{9}{4}\right) + \left(\frac{3}{4}x^2 + 2x - 14\right)
\]

### Step 3: Combine Like Terms

1. **Combine the \(x^2\) terms**:
\[
14x^2 + \frac{3}{4}x^2 = \frac{56}{4}x^2 + \frac{3}{4}x^2 = \frac{59}{4}x^2
\]

2. **Combine the \(x\) terms**:
\[
-3x + 2x = -1x = -x
\]

3. **Combine the constant terms**:
\[
\frac{9}{4} - 14 = \frac{9}{4} - \frac{56}{4} = \frac{9 - 56}{4} = \frac{-47}{4}
\]

### Final Expression

Putting everything together, we have:

\[
\frac{59}{4}x^2 - x - \frac{47}{4}
\]

### Step 4: Express the Entire Expression as a Single Fraction

If you want the entire expression as a single fraction, you can find a common denominator (which is 4):

\[
\frac{59}{4}x^2 - x - \frac{47}{4} = \frac{59}{4}x^2 - \frac{4x}{4} - \frac{47}{4}
\]

Combining them, we get:

\[
\frac{59x^2 - 4x - 47}{4}
\]

### Final Answer

So, the completely fractional form of the expression is:

\[
\boxed{\frac{59x^2 - 4x - 47}{4}}
\]