Question
Solving Quadratic Equations Using Patterns Quick Check
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Question
Gabriel was asked to solve x2−36=0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses
x=6
x equals 6
x=−6
x equals negative 6
x=18, x=−18
x equals 18 , x equals negative 18
x=6, x=−6
x equals 6 , x equals negative 6
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Answers
GPT-4o mini
To solve the equation \( x^2 - 36 = 0 \) using the difference of squares pattern, we can recognize that it can be factored as:
\[
(x - 6)(x + 6) = 0
\]
Setting each factor equal to zero gives us:
1. \( x - 6 = 0 \) → \( x = 6 \)
2. \( x + 6 = 0 \) → \( x = -6 \)
Thus, the correct solutions are:
\[
x = 6 \quad \text{and} \quad x = -6
\]
So the response is:
**x=6, x=−6** (x equals 6, x equals negative 6).
\[
(x - 6)(x + 6) = 0
\]
Setting each factor equal to zero gives us:
1. \( x - 6 = 0 \) → \( x = 6 \)
2. \( x + 6 = 0 \) → \( x = -6 \)
Thus, the correct solutions are:
\[
x = 6 \quad \text{and} \quad x = -6
\]
So the response is:
**x=6, x=−6** (x equals 6, x equals negative 6).