x^4-17x^2+52=0

Solution for x^4-17x^2+52=0 equation:

Simplifying
x4 + -17x2 + 52 = 0

Reorder the terms:
52 + -17x2 + x4 = 0

Solving
52 + -17x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x2)(13 + -1x2) = 0

Factor a difference between two squares.
((2 + x)(2 + -1x))(13 + -1x2) = 0

Subproblem 1
Set the factor '(13 + -1x2)' equal to zero and attempt to solve:

Simplifying
13 + -1x2 = 0

Solving
13 + -1x2 = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x2 = 0 + -13
-1x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-1x2 = -13

Divide each side by '-1'.
x2 = 13

Simplifying
x2 = 13

Take the square root of each side:
x = {-3.605551275, 3.605551275}
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 = {-3.605551275, 3.605551275, -2, 2}