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
x equals 6

Answer 1

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

The equation can be factored as follows:

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

Setting each factor to zero gives us the solutions:

\[ x - 6 = 0 \quad \Rightarrow \quad x = 6 \] \[ x + 6 = 0 \quad \Rightarrow \quad x = -6 \]

Thus, the correct solutions are:

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

So, the correct response from the options provided would be:

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