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=6, x=−6
x equals 6 , x equals negative 6

x=−6
x equals negative 6

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

Answer 1

To solve the equation \(x^2 - 36 = 0\) by factoring using the difference of squares pattern, we can factor the left-hand side as follows:

\[ x^2 - 36 = (x - 6)(x + 6) = 0 \]

Now, we set each factor to zero:

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

Thus, the correct solutions are \(x = 6\) and \(x = -6\).

The correct response is: x=6, x=−6 x equals 6 , x equals negative 6