7x^4+14x^2=693

Solution for 7x^4+14x^2=693 equation:

Simplifying
7x4 + 14x2 = 693

Reorder the terms:
14x2 + 7x4 = 693

Solving
14x2 + 7x4 = 693

Solving for variable 'x'.

Reorder the terms:
-693 + 14x2 + 7x4 = 693 + -693

Combine like terms: 693 + -693 = 0
-693 + 14x2 + 7x4 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-99 + 2x2 + x4) = 0

Factor a trinomial.
7((-11 + -1x2)(9 + -1x2)) = 0

Factor a difference between two squares.
7((-11 + -1x2)((3 + x)(3 + -1x))) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-11 + -1x2)' equal to zero and attempt to solve:

Simplifying
-11 + -1x2 = 0

Solving
-11 + -1x2 = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x2 = 0 + 11
-1x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-1x2 = 11

Divide each side by '-1'.
x2 = -11

Simplifying
x2 = -11

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
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 = {-3, 3}