x^4=16x^2-63

Solution for x^4=16x^2-63 equation:

Simplifying
x4 = 16x2 + -63

Reorder the terms:
x4 = -63 + 16x2

Solving
x4 = -63 + 16x2

Solving for variable 'x'.

Reorder the terms:
63 + -16x2 + x4 = -63 + 16x2 + 63 + -16x2

Reorder the terms:
63 + -16x2 + x4 = -63 + 63 + 16x2 + -16x2

Combine like terms: -63 + 63 = 0
63 + -16x2 + x4 = 0 + 16x2 + -16x2
63 + -16x2 + x4 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
63 + -16x2 + x4 = 0

Factor a trinomial.
(7 + -1x2)(9 + -1x2) = 0

Factor a difference between two squares.
(7 + -1x2)((3 + x)(3 + -1x)) = 0

Subproblem 1
Set the factor '(7 + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + -1x2 = 0

Solving
7 + -1x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x2 = 0 + -7
-1x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1x2 = -7

Divide each side by '-1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}
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 = {-2.645751311, 2.645751311, -3, 3}