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 negative 6

x=6, x=−6
x equals 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 recognize that this can be rewritten as:

$$x^2-6^2=0$$

Using the difference of squares formula $a^2-b^2=(a-b)(a+b)$, we can factor the equation as follows:

$$(x-6)(x+6)=0$$

Setting each factor equal to zero gives us the solutions:

1. $x-6=0$ leads to $x=6$
2. $x+6=0$ leads to $x=-6$

Therefore, the correct solutions are:

$$x=6\text{and}x=-6$$

This matches the option:

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