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Gwen was asked to solve 3x^2 − 20 = 7 by factoring using the difference of squares pattern. What is/are the correct solution(s)?

x = -3, x = 3
x = 3
x = -3
x = 9, x = -9

1 answer

To solve the equation \(3x^2 - 20 = 7\) by factoring using the difference of squares pattern, we first need to rearrange the equation:

  1. Start by moving all terms to one side:

\[ 3x^2 - 20 - 7 = 0 \]

This simplifies to:

\[ 3x^2 - 27 = 0 \]

  1. Next, factor out 3 from the equation:

\[ 3(x^2 - 9) = 0 \]

  1. Now, we can recognize that \(x^2 - 9\) is a difference of squares, which can be factored as:

\[ 3(x - 3)(x + 3) = 0 \]

  1. Using the zero product property, we set each factor equal to zero:

\[ x - 3 = 0 \quad \text{or} \quad x + 3 = 0 \]

This gives us the solutions:

\[ x = 3 \quad \text{and} \quad x = -3 \]

Thus, the correct solutions are:

x = -3, x = 3