Simplify (14x2−3x+2.25)+(0.75x2+2x−14)

Answer 1

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

1. Group the terms:

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

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

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

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

5. Putting it all together: \[ 14.75x^2 - x - 11.75 \]

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

Answer 2

Wrong

Answer 3

Let me go through the simplification step-by-step again to ensure accuracy.

We start with the expression: \[ (14x^2 - 3x + 2.25) + (0.75x^2 + 2x - 14) \]

Now, let's combine the like terms:

1. Quadratic Terms:

   • \(14x^2\) from the first expression
   • \(0.75x^2\) from the second expression

   Combine these: \[ 14x^2 + 0.75x^2 = (14 + 0.75)x^2 = 14.75x^2 \]

2. Linear Terms:

   • \(-3x\) from the first expression
   • \(2x\) from the second expression

   Combine these: \[ -3x + 2x = (-3 + 2)x = -1x = -x \]

3. Constant Terms:

   • \(2.25\) from the first expression
   • \(-14\) from the second expression

   Combine these: \[ 2.25 - 14 = 2.25 - 14 = -11.75 \]

Now we can combine all the results together: \[ 14.75x^2 - x - 11.75 \]

Thus, the correct simplified expression is: \[ \boxed{14.75x^2 - x - 11.75} \]

If there was something else that you needed me to check or clarify, please let me know!