x^4-41x^2+40=0

Solution for x^4-41x^2+40=0 equation:

Simplifying
x4 + -41x2 + 40 = 0

Reorder the terms:
40 + -41x2 + x4 = 0

Solving
40 + -41x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x2)(40 + -1x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(40 + -1x2) = 0

Subproblem 1
Set the factor '(40 + -1x2)' equal to zero and attempt to solve:

Simplifying
40 + -1x2 = 0

Solving
40 + -1x2 = 0

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

Add '-40' to each side of the equation.
40 + -40 + -1x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -1x2 = 0 + -40
-1x2 = 0 + -40

Combine like terms: 0 + -40 = -40
-1x2 = -40

Divide each side by '-1'.
x2 = 40

Simplifying
x2 = 40

Take the square root of each side:
x = {-6.32455532, 6.32455532}
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 = {-6.32455532, 6.32455532, -1, 1}