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

Question

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

Answer 1

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