x^4+2x^2+1=25

Solution for x^4+2x^2+1=25 equation:

Simplifying
x4 + 2x2 + 1 = 25

Reorder the terms:
1 + 2x2 + x4 = 25

Solving
1 + 2x2 + x4 = 25

Solving for variable 'x'.

Reorder the terms:
1 + -25 + 2x2 + x4 = 25 + -25

Combine like terms: 1 + -25 = -24
-24 + 2x2 + x4 = 25 + -25

Combine like terms: 25 + -25 = 0
-24 + 2x2 + x4 = 0

Factor a trinomial.
(-6 + -1x2)(4 + -1x2) = 0

Factor a difference between two squares.
(-6 + -1x2)((2 + x)(2 + -1x)) = 0

Subproblem 1
Set the factor '(-6 + -1x2)' equal to zero and attempt to solve:

Simplifying
-6 + -1x2 = 0

Solving
-6 + -1x2 = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x2 = 0 + 6
-1x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1x2 = 6

Divide each side by '-1'.
x2 = -6

Simplifying
x2 = -6

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-2, 2}