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)

Question

Responses

x=6
x equals 6

x=18, x=−18
x equals 18 , x equals negative 18

x=−6
x equals negative 6

x=6, x=−6

Answer 1

To solve the equation \( x^2 - 36 = 0 \) by factoring using the difference of squares pattern, we recognize that it can be written as:

\[ x^2 - 6^2 = 0 \]

This fits the difference of squares formula \( a^2 - b^2 = (a - b)(a + b) \), where \( a = x \) and \( b = 6 \).

Factoring gives us:

\[ (x - 6)(x + 6) = 0 \]

Setting each factor equal to zero:

1. \( x - 6 = 0 \) leads to \( x = 6 \)
2. \( x + 6 = 0 \) leads to \( x = -6 \)

Thus, the solutions are:

\[ x = 6 \quad \text{and} \quad x = -6 \]

The correct responses from the options provided are:

• \( x = 6 \)
• \( x = -6 \)
• \( x = 6, x = -6 \)

Overall, the correct solution is \( x = 6, x = -6 \).