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.

Guest Jan 21, 2018

#1**0 **

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**

Guest Jan 21, 2018

edited by
Guest
Jan 21, 2018

#1**0 **

Best Answer

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**

Guest Jan 21, 2018

edited by
Guest
Jan 21, 2018