To solve the equation \( \sqrt{2x} + 13 = 27 \), we first isolate the square root on one side:
\[ \sqrt{2x} = 27 - 13 \]
\[ \sqrt{2x} = 14 \]
Next, we square both sides to eliminate the square root:
\[ 2x = 14^2 \]
\[ 2x = 196 \]
Now, we solve for \( x \) by dividing both sides by 2:
\[ x = \frac{196}{2} = 98 \]
Now we check if any of the provided options (25, 9, 49, 16) make the equation true:
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\( x = 25 \): \[ \sqrt{2(25)} + 13 = \sqrt{50} + 13 \neq 27 \]
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\( x = 9 \): \[ \sqrt{2(9)} + 13 = \sqrt{18} + 13 \neq 27 \]
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\( x = 49 \): \[ \sqrt{2(49)} + 13 = \sqrt{98} + 13 \neq 27 \]
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\( x = 16 \): \[ \sqrt{2(16)} + 13 = \sqrt{32} + 13 \neq 27 \]
None of the provided values make the equation true. The correct value of \( x \) that satisfies the equation is 98, which is not among the options listed.
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