4x^4=25x^2-6

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Solution for 4x^4=25x^2-6 equation: 


Simplifying
4x4 = 25x2 + -6

Reorder the terms:
4x4 = -6 + 25x2

Solving
4x4 = -6 + 25x2

Solving for variable 'x'.

Reorder the terms:
6 + -25x2 + 4x4 = -6 + 25x2 + 6 + -25x2

Reorder the terms:
6 + -25x2 + 4x4 = -6 + 6 + 25x2 + -25x2

Combine like terms: -6 + 6 = 0
6 + -25x2 + 4x4 = 0 + 25x2 + -25x2
6 + -25x2 + 4x4 = 25x2 + -25x2

Combine like terms: 25x2 + -25x2 = 0
6 + -25x2 + 4x4 = 0

Factor a trinomial.
(1 + -4x2)(6 + -1x2) = 0

Factor a difference between two squares.
((1 + 2x)(1 + -2x))(6 + -1x2) = 0


Subproblem 1
Set the factor '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}

Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 3
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-2.449489743, 2.449489743, -0.5, 0.5}

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