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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

Best Answer 

 #1
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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
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1+0 Answers

 #1
avatar
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

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