Gabriel was asked to solve x2−36=0

Question

𝑥
2
−
36
=
0
by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses

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

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

x=−6
𝑥
=
−
6
x equals negative 6

x=6

Answer 1

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

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

Setting each factor equal to zero gives us:

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

Thus, the correct solutions to the equation are:

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

Therefore, the correct response is:

x = 6, x = -6