3x^4-19x^2+28=0

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Solution for 3x^4-19x^2+28=0 equation: 


Simplifying
3x4 + -19x2 + 28 = 0

Reorder the terms:
28 + -19x2 + 3x4 = 0

Solving
28 + -19x2 + 3x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -3x2)(4 + -1x2) = 0

Factor a difference between two squares.
(7 + -3x2)((2 + x)(2 + -1x)) = 0


Subproblem 1
Set the factor '(7 + -3x2)' equal to zero and attempt to solve:

Simplifying
7 + -3x2 = 0

Solving
7 + -3x2 = 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 + -3x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x2 = 0 + -7
-3x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-3x2 = -7

Divide each side by '-3'.
x2 = 2.333333333

Simplifying
x2 = 2.333333333

Take the square root of each side:
x = {-1.527525232, 1.527525232}

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1.527525232, 1.527525232, -2, 2}

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