Bot GPT 4-o mini To solve the equation \( 2(x + 4)^2 + 44 = 46 \), we will first isolate the squared term.
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Subtract 44 from both sides: \[ 2(x + 4)^2 + 44 - 44 = 46 - 44 \] which simplifies to: \[ 2(x + 4)^2 = 2 \]
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Next, divide both sides by 2: \[ (x + 4)^2 = 1 \]
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Now, take the square root of both sides. Remember to consider both the positive and negative square roots: \[ x + 4 = 1 \quad \text{or} \quad x + 4 = -1 \]
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Solve for \( x \) in both cases:
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For the first equation: \[ x + 4 = 1 \ x = 1 - 4 \ x = -3 \]
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For the second equation: \[ x + 4 = -1 \ x = -1 - 4 \ x = -5 \]
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The solutions to the quadratic equation are: \[ x = -3 \quad \text{and} \quad x = -5 \]
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