To solve the equation \( 3x^2 - 20 = 7 \), we first want to isolate the \( x^2 \) term.
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Start by adding 20 to both sides of the equation: \[ 3x^2 - 20 + 20 = 7 + 20 \] Which simplifies to: \[ 3x^2 = 27 \]
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Next, divide both sides by 3 to solve for \( x^2 \): \[ x^2 = \frac{27}{3} \] This simplifies to: \[ x^2 = 9 \]
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Now, take the square root of both sides: \[ x = \pm \sqrt{9} \] Which gives: \[ x = \pm 3 \]
Thus, the solutions to the equation \( 3x^2 - 20 = 7 \) are \( x = 3 \) and \( x = -3 \).
Final answer: \[ x = 3 \quad \text{and} \quad x = -3 \]
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