0=625x^4+25x^2-2

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Solution for 0=625x^4+25x^2-2 equation: 


Simplifying
0 = 625x4 + 25x2 + -2

Reorder the terms:
0 = -2 + 25x2 + 625x4

Solving
0 = -2 + 25x2 + 625x4

Solving for variable 'x'.

Combine like terms: 0 + 2 = 2
2 + -25x2 + -625x4 = -2 + 25x2 + 625x4 + 2 + -25x2 + -625x4

Reorder the terms:
2 + -25x2 + -625x4 = -2 + 2 + 25x2 + -25x2 + 625x4 + -625x4

Combine like terms: -2 + 2 = 0
2 + -25x2 + -625x4 = 0 + 25x2 + -25x2 + 625x4 + -625x4
2 + -25x2 + -625x4 = 25x2 + -25x2 + 625x4 + -625x4

Combine like terms: 25x2 + -25x2 = 0
2 + -25x2 + -625x4 = 0 + 625x4 + -625x4
2 + -25x2 + -625x4 = 625x4 + -625x4

Combine like terms: 625x4 + -625x4 = 0
2 + -25x2 + -625x4 = 0

Factor a trinomial.
(1 + -25x2)(2 + 25x2) = 0

Factor a difference between two squares.
((1 + 5x)(1 + -5x))(2 + 25x2) = 0


Subproblem 1
Set the factor '(2 + 25x2)' equal to zero and attempt to solve:

Simplifying
2 + 25x2 = 0

Solving
2 + 25x2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + 25x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 25x2 = 0 + -2
25x2 = 0 + -2

Combine like terms: 0 + -2 = -2
25x2 = -2

Divide each side by '25'.
x2 = -0.08

Simplifying
x2 = -0.08

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 '(1 + 5x)' equal to zero and attempt to solve:

Simplifying
1 + 5x = 0

Solving
1 + 5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5x = 0 + -1
5x = 0 + -1

Combine like terms: 0 + -1 = -1
5x = -1

Divide each side by '5'.
x = -0.2

Simplifying
x = -0.2

Subproblem 3
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2
Solution
x = {-0.2, 0.2}

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