X^4-18X^2+17=0

Solution for X^4-18X^2+17=0 equation:

Simplifying
X4 + -18X2 + 17 = 0

Reorder the terms:
17 + -18X2 + X4 = 0

Solving
17 + -18X2 + X4 = 0

Solving for variable 'X'.

Factor a trinomial.
(1 + -1X2)(17 + -1X2) = 0

Factor a difference between two squares.
((1 + X)(1 + -1X))(17 + -1X2) = 0

Subproblem 1
Set the factor '(17 + -1X2)' equal to zero and attempt to solve:

Simplifying
17 + -1X2 = 0

Solving
17 + -1X2 = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1X2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1X2 = 0 + -17
-1X2 = 0 + -17

Combine like terms: 0 + -17 = -17
-1X2 = -17

Divide each side by '-1'.
X2 = 17

Simplifying
X2 = 17

Take the square root of each side:
X = {-4.123105626, 4.123105626}
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 = {-4.123105626, 4.123105626, -1, 1}