Question
Which of the following quadrilack equations is not solvable by grouping 2x + 14x + 12 = 0 x - 12x + 35 = 0 2x ^2- 2x -10=0 x squared minus 2x + 1 = 0
Answers
GPT-4o mini
To determine which of the given quadratic equations is not solvable by grouping, let’s analyze each equation individually.
1. **Equation**: \( 2x + 14x + 12 = 0 \)
**Simplification**: Combine like terms:
\[
16x + 12 = 0
\]
This is not a quadratic equation, as it is linear.
2. **Equation**: \( x - 12x + 35 = 0 \)
**Simplification**: Combine like terms:
\[
-11x + 35 = 0 \implies 11x = 35
\]
This is also not a quadratic equation, as it is linear.
3. **Equation**: \( 2x^2 - 2x - 10 = 0 \)
This is a quadratic equation and can be solved by factoring, completing the square, or using the quadratic formula.
4. **Equation**: \( x^2 - 2x + 1 = 0 \)
This can also be factored as \( (x - 1)^2 = 0 \), and is clearly a quadratic equation.
From the analysis above:
- The equations \( 2x + 14x + 12 = 0 \) and \( x - 12x + 35 = 0 \) are linear equations and thus not solvable as quadratics by grouping.
- The equations \( 2x^2 - 2x - 10 = 0 \) and \( x^2 - 2x + 1 = 0 \) are quadratic equations.
Since you are looking for the one that is not solvable by grouping in the context of quadratic equations, the correct answer is:
**Both** \( 2x + 14x + 12 = 0 \) **and** \( x - 12x + 35 = 0 \) are not solvable by grouping because they are not quadratic equations. However, if you must choose one, you can pick either of them, as they both have the same issue.
If you are looking for strictly quadratic equations:
- The only equations that are quadratic and can be solved by grouping are \( 2x^2 - 2x - 10 = 0 \) and \( x^2 - 2x + 1 = 0 \).
In summary:
**The quadratic equations that are not solvable by grouping** are \( 2x + 14x + 12 = 0 \) and \( x - 12x + 35 = 0 \).
1. **Equation**: \( 2x + 14x + 12 = 0 \)
**Simplification**: Combine like terms:
\[
16x + 12 = 0
\]
This is not a quadratic equation, as it is linear.
2. **Equation**: \( x - 12x + 35 = 0 \)
**Simplification**: Combine like terms:
\[
-11x + 35 = 0 \implies 11x = 35
\]
This is also not a quadratic equation, as it is linear.
3. **Equation**: \( 2x^2 - 2x - 10 = 0 \)
This is a quadratic equation and can be solved by factoring, completing the square, or using the quadratic formula.
4. **Equation**: \( x^2 - 2x + 1 = 0 \)
This can also be factored as \( (x - 1)^2 = 0 \), and is clearly a quadratic equation.
From the analysis above:
- The equations \( 2x + 14x + 12 = 0 \) and \( x - 12x + 35 = 0 \) are linear equations and thus not solvable as quadratics by grouping.
- The equations \( 2x^2 - 2x - 10 = 0 \) and \( x^2 - 2x + 1 = 0 \) are quadratic equations.
Since you are looking for the one that is not solvable by grouping in the context of quadratic equations, the correct answer is:
**Both** \( 2x + 14x + 12 = 0 \) **and** \( x - 12x + 35 = 0 \) are not solvable by grouping because they are not quadratic equations. However, if you must choose one, you can pick either of them, as they both have the same issue.
If you are looking for strictly quadratic equations:
- The only equations that are quadratic and can be solved by grouping are \( 2x^2 - 2x - 10 = 0 \) and \( x^2 - 2x + 1 = 0 \).
In summary:
**The quadratic equations that are not solvable by grouping** are \( 2x + 14x + 12 = 0 \) and \( x - 12x + 35 = 0 \).