Question

Which of the following quadrilack equations is not solvable by grouping 2x^2+ 14x + 12 = 0 x - 12x + 35 = 0 2x ^2- 2x -10=0 x^2squared minus 2x + 1 = 0

Answer 1

To determine which of the given quadratic equations is not solvable by grouping, let's analyze each one individually.

### Given Quadratic Equations:
1. \( 2x^2 + 14x + 12 = 0 \)
2. \( x^2 - 12x + 35 = 0 \)
3. \( 2x^2 - 2x - 10 = 0 \)
4. \( x^2 - 2x + 1 = 0 \)

### Analyzing Each Equation:

1. **Equation: \( 2x^2 + 14x + 12 = 0 \)**
- This can be factored or solved using the quadratic formula. Grouping might be a bit cumbersome since it's straightforward to factor out a 2:
\[
x^2 + 7x + 6 = 0 \implies (x + 6)(x + 1) = 0
\]
- **This equation is solvable by grouping.**

2. **Equation: \( x^2 - 12x + 35 = 0 \)**
- This can be factored as:
\[
(x - 7)(x - 5) = 0
\]
- **This equation is solvable by grouping.**

3. **Equation: \( 2x^2 - 2x - 10 = 0 \)**
- Dividing all terms by 2 gives:
\[
x^2 - x - 5 = 0
\]
- This does not factor nicely, but it can still be solved using the quadratic formula. Grouping isn't particularly applicable here.
- **This equation is not easily solvable by grouping.**

4. **Equation: \( x^2 - 2x + 1 = 0 \)**
- This can be factored as:
\[
(x - 1)^2 = 0
\]
- **This equation is solvable by grouping.**

### Conclusion:
The equation that is not easily solvable by grouping is:

**\( 2x^2 - 2x - 10 = 0 \)**