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Gabriel was asked to solve x^2-36=0 by factoring using the difference of squares pattern . What is/are the correct solutions?

A. x=18,x=-18
B. x=-6
C. x=6
D. x=6,-6

1 answer

To solve the equation \( x^2 - 36 = 0 \) by factoring using the difference of squares pattern, we recognize that it can be expressed as:

\[ x^2 - 6^2 = 0 \]

This follows the difference of squares formula, \( a^2 - b^2 = (a - b)(a + b) \), where \( a = x \) and \( b = 6 \). Therefore, we can factor the equation as:

\[ (x - 6)(x + 6) = 0 \]

Setting each factor equal to zero gives us the solutions:

  1. \( x - 6 = 0 \) leads to \( x = 6 \)
  2. \( x + 6 = 0 \) leads to \( x = -6 \)

Thus, the solutions are \( x = 6 \) and \( x = -6 \).

The correct answer is:

D. x = 6, -6