10x^4-38x^2+28=0

Solution for 10x^4-38x^2+28=0 equation:

Simplifying
10x4 + -38x2 + 28 = 0

Reorder the terms:
28 + -38x2 + 10x4 = 0

Solving
28 + -38x2 + 10x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -19x2 + 5x4) = 0

Factor a trinomial.
2((1 + -1x2)(14 + -5x2)) = 0

Factor a difference between two squares.
2(((1 + x)(1 + -1x))(14 + -5x2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(14 + -5x2)' equal to zero and attempt to solve:

Simplifying
14 + -5x2 = 0

Solving
14 + -5x2 = 0

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

Add '-14' to each side of the equation.
14 + -14 + -5x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -5x2 = 0 + -14
-5x2 = 0 + -14

Combine like terms: 0 + -14 = -14
-5x2 = -14

Divide each side by '-5'.
x2 = 2.8

Simplifying
x2 = 2.8

Take the square root of each side:
x = {-1.673320053, 1.673320053}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-1.673320053, 1.673320053, -1, 1}