10x^2=x^4+24

Solution for 10x^2=x^4+24 equation:

Simplifying
10x2 = x4 + 24

Reorder the terms:
10x2 = 24 + x4

Solving
10x2 = 24 + x4

Solving for variable 'x'.

Reorder the terms:
-24 + 10x2 + -1x4 = 24 + x4 + -24 + -1x4

Reorder the terms:
-24 + 10x2 + -1x4 = 24 + -24 + x4 + -1x4

Combine like terms: 24 + -24 = 0
-24 + 10x2 + -1x4 = 0 + x4 + -1x4
-24 + 10x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-24 + 10x2 + -1x4 = 0

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

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

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

Simplifying
-6 + x2 = 0

Solving
-6 + x2 = 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 + x2 = 0 + 6

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

Combine like terms: 0 + 6 = 6
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}