0=2x^4-7x^2-49

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Solution for 0=2x^4-7x^2-49 equation: 


Simplifying
0 = 2x4 + -7x2 + -49

Reorder the terms:
0 = -49 + -7x2 + 2x4

Solving
0 = -49 + -7x2 + 2x4

Solving for variable 'x'.

Combine like terms: 0 + 49 = 49
49 + 7x2 + -2x4 = -49 + -7x2 + 2x4 + 49 + 7x2 + -2x4

Reorder the terms:
49 + 7x2 + -2x4 = -49 + 49 + -7x2 + 7x2 + 2x4 + -2x4

Combine like terms: -49 + 49 = 0
49 + 7x2 + -2x4 = 0 + -7x2 + 7x2 + 2x4 + -2x4
49 + 7x2 + -2x4 = -7x2 + 7x2 + 2x4 + -2x4

Combine like terms: -7x2 + 7x2 = 0
49 + 7x2 + -2x4 = 0 + 2x4 + -2x4
49 + 7x2 + -2x4 = 2x4 + -2x4

Combine like terms: 2x4 + -2x4 = 0
49 + 7x2 + -2x4 = 0

Factor a trinomial.
(7 + -1x2)(7 + 2x2) = 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 '(7 + 2x2)' equal to zero and attempt to solve:

Simplifying
7 + 2x2 = 0

Solving
7 + 2x2 = 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 + 2x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x2 = 0 + -7
2x2 = 0 + -7

Combine like terms: 0 + -7 = -7
2x2 = -7

Divide each side by '2'.
x2 = -3.5

Simplifying
x2 = -3.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {-2.645751311, 2.645751311}

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