Question

question
solve for all values of x.
\\(\frac{x}{-8} = \frac{8}{-x}\\)
answer attempt 1 out of 2
\\(\oplus\\) additional solution \\(\circleddash\\) no solution

Explanation:

Step1: Cross-multiply to eliminate fractions

$x \times (-x) = 8 \times (-8)$

Step2: Simplify both sides

$-x^2 = -64$

Step3: Multiply by -1 to isolate $x^2$

$x^2 = 64$

Step4: Take square root of both sides

$x = \pm\sqrt{64}$

Step5: Verify valid solutions

Check $x=8$: $\frac{8}{-8}=-1$, $\frac{8}{-8}=-1$ (valid). Check $x=-8$: $\frac{-8}{-8}=1$, $\frac{8}{8}=1$ (valid).

Answer:

$x = 8$ and $x = -8$