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) Responses x=18, x=−18 x equals 18 , x equals negative 18 x=6, x=−6 x equals 6 , x equals negative 6 x=−6 x equals negative 6 x=6
The correct solutions are x = 6 and x = -6.
To solve the equation x^2 - 36 = 0 using the difference of squares pattern, we need to recognize that it can be written as (x - 6)(x + 6) = 0.
The difference of squares pattern states that when we have a difference of squares like a^2 - b^2, it can be factored as (a - b)(a + b).
So, in this case, x^2 - 36 can be factored as (x - 6)(x + 6) = 0.
To find the solutions, we set each factor equal to zero:
x - 6 = 0
Solving for x, we add 6 to both sides:
x = 6
x + 6 = 0
Solving for x, we subtract 6 from both sides:
x = -6
Therefore, the correct solutions to the equation x^2 - 36 = 0, using the factoring method, are x = 6 and x = -6.
To solve the equation x^2 - 36 = 0 by factoring using the difference of squares pattern, we can rewrite it as (x + 6)(x - 6) = 0.
Setting each factor equal to zero, we get two possible solutions:
x + 6 = 0 => x = -6
x - 6 = 0 => x = 6
Therefore, the correct solutions are x = -6 and x = 6.