0=x^4+3x^2-16

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Solution for 0=x^4+3x^2-16 equation:


Simplifying
0 = x4 + 3x2 + -16

Reorder the terms:
0 = -16 + 3x2 + x4

Solving
0 = -16 + 3x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + 16 = 16
16 + -3x2 + -1x4 = -16 + 3x2 + x4 + 16 + -3x2 + -1x4

Reorder the terms:
16 + -3x2 + -1x4 = -16 + 16 + 3x2 + -3x2 + x4 + -1x4

Combine like terms: -16 + 16 = 0
16 + -3x2 + -1x4 = 0 + 3x2 + -3x2 + x4 + -1x4
16 + -3x2 + -1x4 = 3x2 + -3x2 + x4 + -1x4

Combine like terms: 3x2 + -3x2 = 0
16 + -3x2 + -1x4 = 0 + x4 + -1x4
16 + -3x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
16 + -3x2 + -1x4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + 3x2 + x4 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 3x2 + 16 + x4 = 0 + 16

Reorder the terms:
-16 + 16 + 3x2 + x4 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 3x2 + x4 = 0 + 16
3x2 + x4 = 0 + 16

Combine like terms: 0 + 16 = 16
3x2 + x4 = 16

The x term is 3x2.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x2 + 2.25 + x4 = 16 + 2.25

Reorder the terms:
2.25 + 3x2 + x4 = 16 + 2.25

Combine like terms: 16 + 2.25 = 18.25
2.25 + 3x2 + x4 = 18.25

Factor a perfect square on the left side:
(x2 + 1.5)(x2 + 1.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x2 + 1.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x2 + 1.5 = 4.272001873 Simplifying x2 + 1.5 = 4.272001873 Reorder the terms: 1.5 + x2 = 4.272001873 Solving 1.5 + x2 = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = 4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 4.272001873 + -1.5 x2 = 4.272001873 + -1.5 Combine like terms: 4.272001873 + -1.5 = 2.772001873 x2 = 2.772001873 Simplifying x2 = 2.772001873 Take the square root of each side: x = {-1.664932994, 1.664932994}

Subproblem 2

x2 + 1.5 = -4.272001873 Simplifying x2 + 1.5 = -4.272001873 Reorder the terms: 1.5 + x2 = -4.272001873 Solving 1.5 + x2 = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = -4.272001873 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -4.272001873 + -1.5 x2 = -4.272001873 + -1.5 Combine like terms: -4.272001873 + -1.5 = -5.772001873 x2 = -5.772001873 Simplifying x2 = -5.772001873 Reorder the terms: 5.772001873 + x2 = -5.772001873 + 5.772001873 Combine like terms: -5.772001873 + 5.772001873 = 0.000000000 5.772001873 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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