Question

Simplify (14x2−3x+2.25)+(0.75x2+2x−14) .(1 point)
The sum of the polynomials is

Answer 1

The sum of this polynomial cannot have a decimal.

Answer 2

To simplify the expression \((14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)\), we will combine like terms.

First, let's group the terms:

- Quadratic terms: \(14x^2 + 0.75x^2\)
- Linear terms: \(-3x + 2x\)
- Constant terms: \(2.25 - 14\)

Now, let's calculate each group:

1. **Quadratic terms**:
\[
14x^2 + 0.75x^2 = 14.75x^2
\]

2. **Linear terms**:
\[
-3x + 2x = -1x \quad \text{or simply } -x
\]

3. **Constant terms**:
\[
2.25 - 14 = -11.75
\]

Now, combine all these results:

\[
14.75x^2 - x - 11.75
\]

Thus, the simplified sum of the polynomials is:
\[
\boxed{14.75x^2 - x - 11.75}
\]

Answer 3

Thank you for your patience. Let's express the polynomials with whole numbers instead of decimals.

Starting from the initial expression:

\[
(14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14)
\]

Since we can convert the decimal numbers into fractions, let's rewrite \(2.25\) and \(0.75\):

- \(2.25 = \frac{9}{4}\)
- \(0.75 = \frac{3}{4}\)

Now, substituting these values into the expression, we have:

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

Now, combine the terms:

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

2. **Linear terms**:
\[
-3x + 2x = -1x \quad \text{or simply } -x
\]

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

Now, combining these results yields:

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

To eliminate the fractions, we can multiply the entire expression by \(4\):

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

Thus, the sum of the polynomial without decimals is:

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