Question
Question
Rewrite the following quadratic equation in standard form and then solve by factoring out the GCF: 6x^2=22x
.(1 point)
The smaller solution is x=
, and the larger solution is x=
.
Remaining Attempts : 3
Answers
Answered by
GPT-4o mini
To rewrite the quadratic equation \( 6x^2 = 22x \) in standard form, we first need to move all terms to one side of the equation. This gives us:
\[
6x^2 - 22x = 0
\]
Next, we can factor out the greatest common factor (GCF) from the left-hand side. The GCF of \( 6x^2 \) and \( -22x \) is \( 2x \):
\[
2x(3x - 11) = 0
\]
Now we set each factor equal to zero:
1. \( 2x = 0 \)
2. \( 3x - 11 = 0 \)
From the first factor:
\[
2x = 0 \implies x = 0
\]
From the second factor:
\[
3x - 11 = 0 \implies 3x = 11 \implies x = \frac{11}{3}
\]
Thus, the solutions are:
- The smaller solution is \( x = 0 \).
- The larger solution is \( x = \frac{11}{3} \).
\[
6x^2 - 22x = 0
\]
Next, we can factor out the greatest common factor (GCF) from the left-hand side. The GCF of \( 6x^2 \) and \( -22x \) is \( 2x \):
\[
2x(3x - 11) = 0
\]
Now we set each factor equal to zero:
1. \( 2x = 0 \)
2. \( 3x - 11 = 0 \)
From the first factor:
\[
2x = 0 \implies x = 0
\]
From the second factor:
\[
3x - 11 = 0 \implies 3x = 11 \implies x = \frac{11}{3}
\]
Thus, the solutions are:
- The smaller solution is \( x = 0 \).
- The larger solution is \( x = \frac{11}{3} \).