To solve the equation \( \sqrt{2x} + 13 = 27 \), we first isolate the square root term:
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Subtract 13 from both sides: \[ \sqrt{2x} = 27 - 13 \] \[ \sqrt{2x} = 14 \]
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Now square both sides to eliminate the square root: \[ 2x = 14^2 \] \[ 2x = 196 \]
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Divide both sides by 2 to solve for \( x \): \[ x = \frac{196}{2} \] \[ x = 98 \]
Now, let's check if any of the given options (49, 16, 9, 25) lead us back to \( x = 98 \):
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For \( x = 49 \): \[ 2(49) = 98 \quad \text{and} \quad \sqrt{98} + 13 \neq 27 \]
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For \( x = 16 \): \[ 2(16) = 32 \quad \text{and} \quad \sqrt{32} + 13 \neq 27 \]
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For \( x = 9 \): \[ 2(9) = 18 \quad \text{and} \quad \sqrt{18} + 13 \neq 27 \]
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For \( x = 25 \): \[ 2(25) = 50 \quad \text{and} \quad \sqrt{50} + 13 \neq 27 \]
None of the options provided make the equation true as they do not satisfy \( \sqrt{2x} + 13 = 27 \). Based on our working, the correct answer for \( x \) that satisfies \( \sqrt{2x} + 13 = 27 \) is \( x = 98 \).
It appears that no answer choices correspond to the solution of the original problem.
1 answer