(4x^4-3x^2-1)+(3x^4+6x^2)=

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Solution for (4x^4-3x^2-1)+(3x^4+6x^2)= equation: 


Simplifying
(4x4 + -3x2 + -1) + (3x4 + 6x2) = 0

Reorder the terms:
(-1 + -3x2 + 4x4) + (3x4 + 6x2) = 0

Remove parenthesis around (-1 + -3x2 + 4x4)
-1 + -3x2 + 4x4 + (3x4 + 6x2) = 0

Reorder the terms:
-1 + -3x2 + 4x4 + (6x2 + 3x4) = 0

Remove parenthesis around (6x2 + 3x4)
-1 + -3x2 + 4x4 + 6x2 + 3x4 = 0

Reorder the terms:
-1 + -3x2 + 6x2 + 4x4 + 3x4 = 0

Combine like terms: -3x2 + 6x2 = 3x2
-1 + 3x2 + 4x4 + 3x4 = 0

Combine like terms: 4x4 + 3x4 = 7x4
-1 + 3x2 + 7x4 = 0

Solving
-1 + 3x2 + 7x4 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-0.1428571429 + 0.4285714286x2 + x4 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.4285714286x2 + 0.1428571429 + x4 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 0.4285714286x2 + x4 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 0.4285714286x2 + x4 = 0 + 0.1428571429
0.4285714286x2 + x4 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
0.4285714286x2 + x4 = 0.1428571429

The x term is 0.4285714286x2.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286x2 + 0.04591836735 + x4 = 0.1428571429 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286x2 + x4 = 0.1428571429 + 0.04591836735

Combine like terms: 0.1428571429 + 0.04591836735 = 0.18877551025
0.04591836735 + 0.4285714286x2 + x4 = 0.18877551025

Factor a perfect square on the left side:
(x2 + 0.2142857143)(x2 + 0.2142857143) = 0.18877551025

Calculate the square root of the right side: 0.434483038

Break this problem into two subproblems by setting 
(x2 + 0.2142857143) equal to 0.434483038 and -0.434483038.


Subproblem 1
x2 + 0.2142857143 = 0.434483038

Simplifying
x2 + 0.2142857143 = 0.434483038

Reorder the terms:
0.2142857143 + x2 = 0.434483038

Solving
0.2142857143 + x2 = 0.434483038

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x2 = 0.434483038 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x2 = 0.434483038 + -0.2142857143
x2 = 0.434483038 + -0.2142857143

Combine like terms: 0.434483038 + -0.2142857143 = 0.2201973237
x2 = 0.2201973237

Simplifying
x2 = 0.2201973237

Take the square root of each side:
x = {-0.469251877, 0.469251877}


Subproblem 2
x2 + 0.2142857143 = -0.434483038

Simplifying
x2 + 0.2142857143 = -0.434483038

Reorder the terms:
0.2142857143 + x2 = -0.434483038

Solving
0.2142857143 + x2 = -0.434483038

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x2 = -0.434483038 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x2 = -0.434483038 + -0.2142857143
x2 = -0.434483038 + -0.2142857143

Combine like terms: -0.434483038 + -0.2142857143 = -0.6487687523
x2 = -0.6487687523

Simplifying
x2 = -0.6487687523

Reorder the terms:
0.6487687523 + x2 = -0.6487687523 + 0.6487687523

Combine like terms: -0.6487687523 + 0.6487687523 = 0.0000000000
0.6487687523 + x2 = 0.0000000000

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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