x^4=12x^2-35

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Solution for x^4=12x^2-35 equation: 


Simplifying
x4 = 12x2 + -35

Reorder the terms:
x4 = -35 + 12x2

Solving
x4 = -35 + 12x2

Solving for variable 'x'.

Reorder the terms:
35 + -12x2 + x4 = -35 + 12x2 + 35 + -12x2

Reorder the terms:
35 + -12x2 + x4 = -35 + 35 + 12x2 + -12x2

Combine like terms: -35 + 35 = 0
35 + -12x2 + x4 = 0 + 12x2 + -12x2
35 + -12x2 + x4 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
35 + -12x2 + x4 = 0

Factor a trinomial.
(5 + -1x2)(7 + -1x2) = 0


Subproblem 1
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}

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 = {-2.236067978, 2.236067978, -2.645751311, 2.645751311}

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