Solve the equation by identifying the quadratic form. Use a]substitute variable and find all real solutions by factoring. (Enter your answers as a comma-separated list.)
\[
x^{4}-82 x^{2}+81=0
\]
Answer
Final Answer: The solutions to the equation are \(\boxed{-1, 1, -9, 9}\)
Step 1 ：Given the equation \(x^{4}-82 x^{2}+81=0\)
Step 2 ：Notice that this is a quadratic equation in disguise. If we let \(y = x^2\), the equation becomes \(y^2 - 82y + 81 = 0\), which is a standard quadratic equation.
Step 3 ：Solve this equation by factoring to get \(y = 1, 81\)
Step 4 ：Substitute \(x^2\) back in for \(y\) to find the solutions for \(x\). This gives us \(x^2 = 1, 81\)
Step 5 ：Solving for \(x\) gives us \(x = -1, 1, -9, 9\)
Step 6 ：Final Answer: The solutions to the equation are \(\boxed{-1, 1, -9, 9}\)
