Question
Gwen was asked to solve 3x2−20=7 by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses
x=−3, x=3
x equals negative 3 , x equals 3
x=3
x equals 3
x=−3
x equals negative 3
x=9, x=−9
Responses
x=−3, x=3
x equals negative 3 , x equals 3
x=3
x equals 3
x=−3
x equals negative 3
x=9, x=−9
Answers
GPT-4o mini
To solve the equation \( 3x^2 - 20 = 7 \) by factoring, we first need to rearrange it:
1. Subtract 7 from both sides:
\[
3x^2 - 20 - 7 = 0 \Rightarrow 3x^2 - 27 = 0
\]
2. Factor out 3:
\[
3(x^2 - 9) = 0
\]
3. Next, we can apply the difference of squares pattern as follows:
\[
x^2 - 9 = 0
\]
which can be factored as:
\[
(x - 3)(x + 3) = 0
\]
4. Setting each factor to zero gives us the solutions:
\[
x - 3 = 0 \Rightarrow x = 3
\]
\[
x + 3 = 0 \Rightarrow x = -3
\]
Thus, the solutions to the original equation \( 3x^2 - 20 = 7 \) are \( x = -3 \) and \( x = 3 \).
The correct response is:
**x=−3, x=3** (or in textual response: x equals negative 3, x equals 3).
1. Subtract 7 from both sides:
\[
3x^2 - 20 - 7 = 0 \Rightarrow 3x^2 - 27 = 0
\]
2. Factor out 3:
\[
3(x^2 - 9) = 0
\]
3. Next, we can apply the difference of squares pattern as follows:
\[
x^2 - 9 = 0
\]
which can be factored as:
\[
(x - 3)(x + 3) = 0
\]
4. Setting each factor to zero gives us the solutions:
\[
x - 3 = 0 \Rightarrow x = 3
\]
\[
x + 3 = 0 \Rightarrow x = -3
\]
Thus, the solutions to the original equation \( 3x^2 - 20 = 7 \) are \( x = -3 \) and \( x = 3 \).
The correct response is:
**x=−3, x=3** (or in textual response: x equals negative 3, x equals 3).