Find all real values of $x$ that satisfy the equation $(x^2 - 82)^2 = 324$. If you find more than one, then list your values in increasing order, separated by commas.
Solve for x:
(x^2 - 82)^2 = 324
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x^2 - 82 = 18 or x^2 - 82 = -18
Look at the first equation: Isolate terms with x to the left hand side.
Add 82 to both sides:
x^2 = 100 or x^2 - 82 = -18
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x = 10 or x = -10 or x^2 - 82 = -18
Look at the third equation: Isolate terms with x to the left hand side.
Add 82 to both sides:
x = 10 or x = -10 or x^2 = 64
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x = 10 or x = -10 or x = 8 or x = -8
Solve for x:
(x^2 - 82)^2 = 324
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x^2 - 82 = 18 or x^2 - 82 = -18
Look at the first equation: Isolate terms with x to the left hand side.
Add 82 to both sides:
x^2 = 100 or x^2 - 82 = -18
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x = 10 or x = -10 or x^2 - 82 = -18
Look at the third equation: Isolate terms with x to the left hand side.
Add 82 to both sides:
x = 10 or x = -10 or x^2 = 64
Eliminate the exponent on the left hand side.
Take the square root of both sides:
x = 10 or x = -10 or x = 8 or x = -8
