Bot GPT 4-o mini To solve the equation \( 2(x - 5)^2 + 2 = 20 \), we will first simplify the equation step by step.
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Start with the original equation: \[ 2(x - 5)^2 + 2 = 20 \]
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Subtract 2 from both sides: \[ 2(x - 5)^2 = 18 \]
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Divide both sides by 2: \[ (x - 5)^2 = 9 \]
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Now take the square root of both sides: \[ x - 5 = \pm 3 \]
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This gives us two equations: \[ x - 5 = 3 \quad \text{or} \quad x - 5 = -3 \]
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Solving these equations:
- For \( x - 5 = 3 \): \[ x = 8 \]
- For \( x - 5 = -3 \): \[ x = 2 \]
Thus, the solutions are \( x = 8 \) and \( x = 2 \).
Therefore, there are two solutions in the solution set.
The answer is: two
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