Question
Which of the following quadrilack equations is not solvable by grouping 2x + 14x + 12 = 0 x - 12x + 35 = 0 2x - 2x -10=0 x squared minus 2x + 1 = 0
Answers
GPT-4o mini
To determine which of the given equations is not solvable by grouping, let's analyze them one by one.
1. **\(2x + 14x + 12 = 0\)**
Combine like terms:
\(16x + 12 = 0\)
This can be rearranged to solve for \(x\):
\(x = -\frac{12}{16} = -\frac{3}{4}\)
This is solvable.
2. **\(x - 12x + 35 = 0\)**
Combine like terms:
\(-11x + 35 = 0\)
Rearranging gives:
\(x = \frac{35}{11}\)
This is solvable.
3. **\(2x - 2x - 10 = 0\)**
Combine like terms:
\(0 - 10 = 0\)
This simplifies to \(-10 = 0\), which is false.
Thus, this equation has no solutions.
4. **\(x^2 - 2x + 1 = 0\)**
This can be factored:
\((x - 1)^2 = 0\)
Giving \(x = 1\) as a double root.
This is solvable.
From the analysis, the equation that is not solvable by grouping (or solvable at all) is:
**\(2x - 2x - 10 = 0\)**.
1. **\(2x + 14x + 12 = 0\)**
Combine like terms:
\(16x + 12 = 0\)
This can be rearranged to solve for \(x\):
\(x = -\frac{12}{16} = -\frac{3}{4}\)
This is solvable.
2. **\(x - 12x + 35 = 0\)**
Combine like terms:
\(-11x + 35 = 0\)
Rearranging gives:
\(x = \frac{35}{11}\)
This is solvable.
3. **\(2x - 2x - 10 = 0\)**
Combine like terms:
\(0 - 10 = 0\)
This simplifies to \(-10 = 0\), which is false.
Thus, this equation has no solutions.
4. **\(x^2 - 2x + 1 = 0\)**
This can be factored:
\((x - 1)^2 = 0\)
Giving \(x = 1\) as a double root.
This is solvable.
From the analysis, the equation that is not solvable by grouping (or solvable at all) is:
**\(2x - 2x - 10 = 0\)**.