Gabriel was asked to solve x^2 - 36 = 0 by factoring using the difference of squares pattern. What is/are the correct solution(s)?
A. x = 6. x = -6
B. x = 18, x = -18
C. x = -6
D. x = 6
A. x = 6. x = -6
To solve the equation x^2 - 36 = 0 using the difference of squares pattern, we need to rewrite the equation so that it factors into the difference of squares. The difference of squares pattern states that for any two numbers a and b, the equation a^2 - b^2 can be factored as (a + b)(a - b).
In this case, we have x^2 - 36 = 0. The square root of 36 is 6, so we can rewrite the equation as (x + 6)(x - 6) = 0.
Now, we have a product of two terms equal to zero. According to the zero product property, this means that either the first term (x + 6) is zero, or the second term (x - 6) is zero.
Setting each term equal to zero, we get:
x + 6 = 0, which gives us x = -6
x - 6 = 0, which gives us x = 6
Therefore, the correct solution is: x = 6 and x = -6. This matches option A: x = 6, x = -6.
To solve the equation x^2 - 36 = 0 using the difference of squares pattern, you can rewrite the equation as (x + 6)(x - 6) = 0.
Now, to find the solutions, set each factor equal to zero and solve for x:
x + 6 = 0 or x - 6 = 0.
For the first equation x + 6 = 0, subtract 6 from both sides to get x = -6.
For the second equation x - 6 = 0, add 6 to both sides to get x = 6.
Therefore, the correct solutions are x = -6 and x = 6. So, the correct answer is A. x = 6, x = -6.