Solving Quadratic Equations Using Patterns Quick Check

Question

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Question
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=6
x equals 6

x=−6
x equals negative 6

x=18, x=−18
x equals 18 , x equals negative 18

x=6, x=−6
x equals 6 , x equals negative 6
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Answer 1

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

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

Setting each factor equal to zero gives us:

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

Thus, the correct solutions are:

\[ x = 6 \quad \text{and} \quad x = -6 \]

So the response is:

x=6, x=−6 (x equals 6, x equals negative 6).