Gabriel was asked to solve x2−36=0

Question

by factoring using the difference of squares pattern. What is/are the correct solution(s)?(1 point)
Responses

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

x=6

Answer 1

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

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

Setting this equal to zero gives us:

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

Now we can solve for \( x \) by setting each factor to zero:

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

Therefore, the correct solutions are:

\( x = 6 \) and \( x = -6 \)

The correct response is:

x = 6, x = -6 or x equals 6, x equals negative 6.