Let's solve the equation [tex]\(\frac{2}{x} = \frac{x}{32}\)[/tex] step by step.
1. Set up the equation:
[tex]\[
\frac{2}{x} = \frac{x}{32}
\][/tex]
2. Cross-multiply to eliminate the fractions:
[tex]\[
2 \cdot 32 = x \cdot x
\][/tex]
This simplifies to:
[tex]\[
64 = x^2
\][/tex]
3. Solve for [tex]\(x\)[/tex] by taking the square root of both sides:
[tex]\[
x^2 = 64
\][/tex]
4. Take the square root of both sides:
[tex]\[
x = \pm \sqrt{64}
\][/tex]
[tex]\[
x = \pm 8
\][/tex]
Therefore, the solutions to the equation [tex]\(\frac{2}{x} = \frac{x}{32}\)[/tex] are:
[tex]\[
x = -8 \quad \text{and} \quad x = 8
\][/tex]
