Question
Solve the quadratic equation 84x2+16x=0
by factoring out the GCF.(1 point)
Responses
The solutions are x=0
and x=421
.
The solutions are x equals 0 and x equals Start Fraction 4 over 21 End Fraction .
The solutions are x=−421
and x=0
.
The solutions are x equals negative Start Fraction 4 over 21 End Fraction and x equals 0 .
The solutions are x=−4
and x=−421
.
The solutions are x equals negative 4 and x equals negative Start Fraction 4 over 21 End Fraction .
The solutions are x=0
and x=4
.
by factoring out the GCF.(1 point)
Responses
The solutions are x=0
and x=421
.
The solutions are x equals 0 and x equals Start Fraction 4 over 21 End Fraction .
The solutions are x=−421
and x=0
.
The solutions are x equals negative Start Fraction 4 over 21 End Fraction and x equals 0 .
The solutions are x=−4
and x=−421
.
The solutions are x equals negative 4 and x equals negative Start Fraction 4 over 21 End Fraction .
The solutions are x=0
and x=4
.
Answers
Answer
pick a anwser
Answer
thats not a anwser
Answer
Which of the following quadratic equations is not solvable by grouping?(1 point)
Responses
x2−12x+35=0
x squared minus 12 x plus 35 equals 0
2x2+14x+12=0
2 x squared plus 14 x plus 12 equals 0
2x2−2x−10=0
2 x squared minus 2 x minus 10 equals 0
x2−2x+1=0
Responses
x2−12x+35=0
x squared minus 12 x plus 35 equals 0
2x2+14x+12=0
2 x squared plus 14 x plus 12 equals 0
2x2−2x−10=0
2 x squared minus 2 x minus 10 equals 0
x2−2x+1=0
Answered by
GPT-4o mini
To solve the quadratic equation \( 84x^2 + 16x = 0 \) by factoring out the greatest common factor (GCF), let's start by identifying the GCF of the two terms:
1. The GCF of \( 84x^2 \) and \( 16x \) is \( 4x \).
Now, factor out \( 4x \):
\[
84x^2 + 16x = 4x(21x + 4) = 0
\]
Next, we can set each factor equal to zero:
1. \( 4x = 0 \) leads to:
\[
x = 0
\]
2. \( 21x + 4 = 0 \) leads to:
\[
21x = -4 \\
x = -\frac{4}{21}
\]
Thus, the solutions to the equation \( 84x^2 + 16x = 0 \) are:
\[
x = 0 \quad \text{and} \quad x = -\frac{4}{21}
\]
The correct response is:
**The solutions are \( x = 0 \) and \( x = -\frac{4}{21} \).**
1. The GCF of \( 84x^2 \) and \( 16x \) is \( 4x \).
Now, factor out \( 4x \):
\[
84x^2 + 16x = 4x(21x + 4) = 0
\]
Next, we can set each factor equal to zero:
1. \( 4x = 0 \) leads to:
\[
x = 0
\]
2. \( 21x + 4 = 0 \) leads to:
\[
21x = -4 \\
x = -\frac{4}{21}
\]
Thus, the solutions to the equation \( 84x^2 + 16x = 0 \) are:
\[
x = 0 \quad \text{and} \quad x = -\frac{4}{21}
\]
The correct response is:
**The solutions are \( x = 0 \) and \( x = -\frac{4}{21} \).**
Answered by
GPT-4o mini
The correct answer is:
**The solutions are \( x = 0 \) and \( x = -\frac{4}{21} \).**
**The solutions are \( x = 0 \) and \( x = -\frac{4}{21} \).**
Answered by
GPT-4o mini
I apologize for the misunderstanding. Based on your options, the correct choice is:
**The solutions are \( x = -\frac{4}{21} \) and \( x = 0 \).**
**The solutions are \( x = -\frac{4}{21} \) and \( x = 0 \).**
Answered by
GPT-4o mini
To determine which quadratic equation is not solvable by grouping, we can analyze each option to see if they can be factored into two binomials (which is typically how grouping works).
1. **\(x^2 - 12x + 35 = 0\)**
- This factors to \((x - 5)(x - 7) = 0\).
2. **\(2x^2 + 14x + 12 = 0\)**
- First factor out the GCF (2):
\[2(x^2 + 7x + 6) = 0\]
- Then factor the quadratic:
\[(x + 1)(x + 6) = 0\]
- Thus, this is also solvable by grouping.
3. **\(2x^2 - 2x - 10 = 0\)**
- First factor out the GCF (2):
\[2(x^2 - x - 5) = 0\]
- The quadratic \(x^2 - x - 5\) cannot be factored into nice integers, so we would typically use the quadratic formula instead.
4. **\(x^2 - 2x + 1 = 0\)**
- This factors to \((x - 1)(x - 1) = 0\) or \((x - 1)^2 = 0\).
From the above analysis, the quadratic equation that is **not solvable by grouping** is:
**\(2x^2 - 2x - 10 = 0\)**.
1. **\(x^2 - 12x + 35 = 0\)**
- This factors to \((x - 5)(x - 7) = 0\).
2. **\(2x^2 + 14x + 12 = 0\)**
- First factor out the GCF (2):
\[2(x^2 + 7x + 6) = 0\]
- Then factor the quadratic:
\[(x + 1)(x + 6) = 0\]
- Thus, this is also solvable by grouping.
3. **\(2x^2 - 2x - 10 = 0\)**
- First factor out the GCF (2):
\[2(x^2 - x - 5) = 0\]
- The quadratic \(x^2 - x - 5\) cannot be factored into nice integers, so we would typically use the quadratic formula instead.
4. **\(x^2 - 2x + 1 = 0\)**
- This factors to \((x - 1)(x - 1) = 0\) or \((x - 1)^2 = 0\).
From the above analysis, the quadratic equation that is **not solvable by grouping** is:
**\(2x^2 - 2x - 10 = 0\)**.