5x^4-500=0

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Solution for 5x^4-500=0 equation: 


Simplifying
5x4 + -500 = 0

Reorder the terms:
-500 + 5x4 = 0

Solving
-500 + 5x4 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '500' to each side of the equation.
-500 + 500 + 5x4 = 0 + 500

Combine like terms: -500 + 500 = 0
0 + 5x4 = 0 + 500
5x4 = 0 + 500

Combine like terms: 0 + 500 = 500
5x4 = 500

Divide each side by '5'.
x4 = 100

Simplifying
x4 = 100

Reorder the terms:
-100 + x4 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + x4 = 0

Factor a difference between two squares.
(10 + x2)(-10 + x2) = 0


Subproblem 1
Set the factor '(10 + x2)' equal to zero and attempt to solve:

Simplifying
10 + x2 = 0

Solving
10 + x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '-10' to each side of the equation.
10 + -10 + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x2 = 0 + -10
x2 = 0 + -10

Combine like terms: 0 + -10 = -10
x2 = -10

Simplifying
x2 = -10

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-10 + x2)' equal to zero and attempt to solve:

Simplifying
-10 + x2 = 0

Solving
-10 + x2 = 0

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x2 = 0 + 10
x2 = 0 + 10

Combine like terms: 0 + 10 = 10
x2 = 10

Simplifying
x2 = 10

Take the square root of each side:
x = {-3.16227766, 3.16227766}
Solution
x = {-3.16227766, 3.16227766}

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