Question

Which of the following values of x makes the equation 2x−−√+13=27 true?(1 point)
Responses

25
25

9
9

49
49

16

Answer 1

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:

1. \( x = 25 \):
\[
\sqrt{2(25)} + 13 = \sqrt{50} + 13 \neq 27
\]

2. \( x = 9 \):
\[
\sqrt{2(9)} + 13 = \sqrt{18} + 13 \neq 27
\]

3. \( x = 49 \):
\[
\sqrt{2(49)} + 13 = \sqrt{98} + 13 \neq 27
\]

4. \( x = 16 \):
\[
\sqrt{2(16)} + 13 = \sqrt{32} + 13 \neq 27
\]

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.