8x^4=14x^2-3

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Solution for 8x^4=14x^2-3 equation: 


Simplifying
8x4 = 14x2 + -3

Reorder the terms:
8x4 = -3 + 14x2

Solving
8x4 = -3 + 14x2

Solving for variable 'x'.

Reorder the terms:
3 + -14x2 + 8x4 = -3 + 14x2 + 3 + -14x2

Reorder the terms:
3 + -14x2 + 8x4 = -3 + 3 + 14x2 + -14x2

Combine like terms: -3 + 3 = 0
3 + -14x2 + 8x4 = 0 + 14x2 + -14x2
3 + -14x2 + 8x4 = 14x2 + -14x2

Combine like terms: 14x2 + -14x2 = 0
3 + -14x2 + 8x4 = 0

Factor a trinomial.
(1 + -4x2)(3 + -2x2) = 0

Factor a difference between two squares.
((1 + 2x)(1 + -2x))(3 + -2x2) = 0


Subproblem 1
Set the factor '(3 + -2x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x2 = 0

Solving
3 + -2x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x2 = 0 + -3
-2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2x2 = -3

Divide each side by '-2'.
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}

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 = {-1.224744871, 1.224744871, -0.5, 0.5}

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