Gabriel was asked to solve x² - 36 = 0 by factoring using the difference of squares pattern. What is/are the correct solutions?
To solve the equation x² - 36 = 0 by factoring using the difference of squares pattern, we first rewrite it as the difference of two perfect squares: (x + 6)(x - 6) = 0.
To set each factor equal to zero and solve for x, we have two equations:
x + 6 = 0, which gives x = -6.
x - 6 = 0, which gives x = 6.
Therefore, the correct solutions are x = -6 and x = 6.
To solve the equation x² - 36 = 0 using the difference of squares pattern, you can write it as (x - 6)(x + 6) = 0. According to the difference of squares pattern, a² - b² = (a - b)(a + b).
Now, set each factor equal to zero and solve for x:
x - 6 = 0 or x + 6 = 0
Solving the first equation:
x - 6 = 0
x = 6
Solving the second equation:
x + 6 = 0
x = -6
Therefore, the correct solutions are x = 6 and x = -6.
To solve the equation x² - 36 = 0 using the difference of squares pattern, first, we need to express the equation as a difference of squares. The difference of squares pattern is a² - b² = (a + b)(a - b), where a and b are numbers or expressions.
In this case, we have x² - 36 = 0. Recognizing that 36 is a perfect square, we can rewrite the equation as (x² - 6²) = 0.
Now we can apply the difference of squares pattern:
(x - 6)(x + 6) = 0
The next step is to set each factor equal to zero and solve for x:
x - 6 = 0 or x + 6 = 0
Solving these equations, we find:
x = 6 or x = -6
Therefore, the correct solutions to the equation x² - 36 = 0 are x = 6 and x = -6.