x^2(x^2-17)=-72

Solution for x^2(x^2-17)=-72 equation:

Simplifying
x2(x2 + -17) = -72

Reorder the terms:
x2(-17 + x2) = -72
(-17 * x2 + x2 * x2) = -72
(-17x2 + x4) = -72

Solving
-17x2 + x4 = -72

Solving for variable 'x'.

Reorder the terms:
72 + -17x2 + x4 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + -17x2 + x4 = 0

Factor a trinomial.
(8 + -1x2)(9 + -1x2) = 0

Factor a difference between two squares.
(8 + -1x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(8 + -1x2)' equal to zero and attempt to solve:

Simplifying
8 + -1x2 = 0

Solving
8 + -1x2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x2 = 0 + -8
-1x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1x2 = -8

Divide each side by '-1'.
x2 = 8

Simplifying
x2 = 8

Take the square root of each side:
x = {-2.828427125, 2.828427125}
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-2.828427125, 2.828427125, -3, 3}