To solve the equation [tex]\(\sqrt{\frac{32.4}{x}} = 2\)[/tex], we can follow these steps:
1. Remove the square root by squaring both sides:
[tex]\[
\left(\sqrt{\frac{32.4}{x}}\right)^2 = 2^2
\][/tex]
This simplifies to:
[tex]\[
\frac{32.4}{x} = 4
\][/tex]
2. Isolate the variable [tex]\(x\)[/tex]:
To solve for [tex]\(x\)[/tex], multiply both sides of the equation by [tex]\(x\)[/tex]:
[tex]\[
32.4 = 4x
\][/tex]
3. Divide by 4 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{32.4}{4}
\][/tex]
4. Calculate the value of [tex]\(x\)[/tex]:
[tex]\[
x = 8.1
\][/tex]
5. Find [tex]\(x - 0.1\)[/tex]:
[tex]\[
x - 0.1 = 8.1 - 0.1 = 8.0
\][/tex]
Therefore, the value of [tex]\(x - 0.1\)[/tex] is [tex]\(\boxed{8.0}\)[/tex].
