To find the value of \( x \) using the geometric mean of the numbers 3 and 4, we can use the formula for the geometric mean, which is given by:
\[ \text{Geometric Mean} = \sqrt{a \times b} \]
where \( a = 3 \) and \( b = 4 \).
Now, let's calculate the geometric mean:
\[ \text{Geometric Mean} = \sqrt{3 \times 4} = \sqrt{12} \]
Next, we can simplify \( \sqrt{12} \):
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
Now we can calculate the numerical value of \( 2\sqrt{3} \). Since \( \sqrt{3} \approx 1.732 \):
\[ 2\sqrt{3} \approx 2 \times 1.732 \approx 3.464 \]
Rounding to the nearest tenth:
\[ 3.464 \approx 3.5 \]
Therefore, the value of \( x \) is approximately:
\[ \boxed{3.5} \]