0=x^4-49x^2

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


Simplifying
0 = x4 + -49x2

Reorder the terms:
0 = -49x2 + x4

Solving
0 = -49x2 + x4

Solving for variable 'x'.
Remove the zero:
49x2 + -1x4 = -49x2 + x4 + 49x2 + -1x4

Reorder the terms:
49x2 + -1x4 = -49x2 + 49x2 + x4 + -1x4

Combine like terms: -49x2 + 49x2 = 0
49x2 + -1x4 = 0 + x4 + -1x4
49x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
49x2 + -1x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(49 + -1x2) = 0

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


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7

Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

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

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

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

Simplifying
x = 7
Solution
x = {0, -7, 7}

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