14x^2=x^4+49

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Solution for 14x^2=x^4+49 equation: 


Simplifying
14x2 = x4 + 49

Reorder the terms:
14x2 = 49 + x4

Solving
14x2 = 49 + x4

Solving for variable 'x'.

Reorder the terms:
-49 + 14x2 + -1x4 = 49 + x4 + -49 + -1x4

Reorder the terms:
-49 + 14x2 + -1x4 = 49 + -49 + x4 + -1x4

Combine like terms: 49 + -49 = 0
-49 + 14x2 + -1x4 = 0 + x4 + -1x4
-49 + 14x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-49 + 14x2 + -1x4 = 0

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


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

Simplifying
-7 + x2 = 0

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

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

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

Simplifying
x2 = 7

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

Subproblem 2
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}
Solution
x = {-2.645751311, 2.645751311, -2.645751311, 2.645751311}

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