x^4+10=10x^2-14

Solution for x^4+10=10x^2-14 equation:

Simplifying
x4 + 10 = 10x2 + -14

Reorder the terms:
10 + x4 = 10x2 + -14

Reorder the terms:
10 + x4 = -14 + 10x2

Solving
10 + x4 = -14 + 10x2

Solving for variable 'x'.

Reorder the terms:
10 + 14 + -10x2 + x4 = -14 + 10x2 + 14 + -10x2

Combine like terms: 10 + 14 = 24
24 + -10x2 + x4 = -14 + 10x2 + 14 + -10x2

Reorder the terms:
24 + -10x2 + x4 = -14 + 14 + 10x2 + -10x2

Combine like terms: -14 + 14 = 0
24 + -10x2 + x4 = 0 + 10x2 + -10x2
24 + -10x2 + x4 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
24 + -10x2 + x4 = 0

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

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

Take the square root of each side:
x = {-2.449489743, 2.449489743}
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 = {-2.449489743, 2.449489743, -2, 2}