To solve the equation \( 3x^2 - 20 = 7 \) by factoring, let's first rearrange it into standard form:
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Move 7 to the left side: \[ 3x^2 - 20 - 7 = 0 \] This simplifies to: \[ 3x^2 - 27 = 0 \]
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Now, factor out the common term: \[ 3(x^2 - 9) = 0 \]
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Identify the difference of squares: \[ x^2 - 9 = (x - 3)(x + 3) \] Therefore, we have: \[ 3(x - 3)(x + 3) = 0 \]
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Set each factor equal to zero: \[ x - 3 = 0 \quad \Rightarrow \quad x = 3 \] \[ x + 3 = 0 \quad \Rightarrow \quad x = -3 \]
The solutions are:
- \( x = 3 \)
- \( x = -3 \)
In summary, the correct response is: x equals 3, x equals negative 3.