x^4+100=25x^2

Solution for x^4+100=25x^2 equation:

Simplifying
x4 + 100 = 25x2

Reorder the terms:
100 + x4 = 25x2

Solving
100 + x4 = 25x2

Solving for variable 'x'.

Reorder the terms:
100 + -25x2 + x4 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
100 + -25x2 + x4 = 0

Factor a trinomial.
(5 + -1x2)(20 + -1x2) = 0

Subproblem 1
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(20 + -1x2)' equal to zero and attempt to solve:

Simplifying
20 + -1x2 = 0

Solving
20 + -1x2 = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x2 = 0 + -20
-1x2 = 0 + -20

Combine like terms: 0 + -20 = -20
-1x2 = -20

Divide each side by '-1'.
x2 = 20

Simplifying
x2 = 20

Take the square root of each side:
x = {-4.472135955, 4.472135955}
Solution
x = {-2.236067978, 2.236067978, -4.472135955, 4.472135955}