4x^2=-3x^4-24x^2+144

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Solution for 4x^2=-3x^4-24x^2+144 equation: 


Simplifying
4x2 = -3x4 + -24x2 + 144

Reorder the terms:
4x2 = 144 + -24x2 + -3x4

Solving
4x2 = 144 + -24x2 + -3x4

Solving for variable 'x'.

Reorder the terms:
-144 + 4x2 + 24x2 + 3x4 = 144 + -24x2 + -3x4 + -144 + 24x2 + 3x4

Combine like terms: 4x2 + 24x2 = 28x2
-144 + 28x2 + 3x4 = 144 + -24x2 + -3x4 + -144 + 24x2 + 3x4

Reorder the terms:
-144 + 28x2 + 3x4 = 144 + -144 + -24x2 + 24x2 + -3x4 + 3x4

Combine like terms: 144 + -144 = 0
-144 + 28x2 + 3x4 = 0 + -24x2 + 24x2 + -3x4 + 3x4
-144 + 28x2 + 3x4 = -24x2 + 24x2 + -3x4 + 3x4

Combine like terms: -24x2 + 24x2 = 0
-144 + 28x2 + 3x4 = 0 + -3x4 + 3x4
-144 + 28x2 + 3x4 = -3x4 + 3x4

Combine like terms: -3x4 + 3x4 = 0
-144 + 28x2 + 3x4 = 0

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

Divide each side by '3'.
-48 + 9.333333333x2 + x4 = 0

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 9.333333333x2 + 48 + x4 = 0 + 48

Reorder the terms:
-48 + 48 + 9.333333333x2 + x4 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 9.333333333x2 + x4 = 0 + 48
9.333333333x2 + x4 = 0 + 48

Combine like terms: 0 + 48 = 48
9.333333333x2 + x4 = 48

The x term is 9.333333333x2.  Take half its coefficient (4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
9.333333333x2 + 21.77777778 + x4 = 48 + 21.77777778

Reorder the terms:
21.77777778 + 9.333333333x2 + x4 = 48 + 21.77777778

Combine like terms: 48 + 21.77777778 = 69.77777778
21.77777778 + 9.333333333x2 + x4 = 69.77777778

Factor a perfect square on the left side:
(x2 + 4.666666667)(x2 + 4.666666667) = 69.77777778

Calculate the square root of the right side: 8.353309391

Break this problem into two subproblems by setting 
(x2 + 4.666666667) equal to 8.353309391 and -8.353309391.


Subproblem 1
x2 + 4.666666667 = 8.353309391

Simplifying
x2 + 4.666666667 = 8.353309391

Reorder the terms:
4.666666667 + x2 = 8.353309391

Solving
4.666666667 + x2 = 8.353309391

Solving for variable 'x'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + x2 = 8.353309391 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x2 = 8.353309391 + -4.666666667
x2 = 8.353309391 + -4.666666667

Combine like terms: 8.353309391 + -4.666666667 = 3.686642724
x2 = 3.686642724

Simplifying
x2 = 3.686642724

Take the square root of each side:
x = {-1.920063208, 1.920063208}


Subproblem 2
x2 + 4.666666667 = -8.353309391

Simplifying
x2 + 4.666666667 = -8.353309391

Reorder the terms:
4.666666667 + x2 = -8.353309391

Solving
4.666666667 + x2 = -8.353309391

Solving for variable 'x'.

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

Add '-4.666666667' to each side of the equation.
4.666666667 + -4.666666667 + x2 = -8.353309391 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + x2 = -8.353309391 + -4.666666667
x2 = -8.353309391 + -4.666666667

Combine like terms: -8.353309391 + -4.666666667 = -13.019976058
x2 = -13.019976058

Simplifying
x2 = -13.019976058

Reorder the terms:
13.019976058 + x2 = -13.019976058 + 13.019976058

Combine like terms: -13.019976058 + 13.019976058 = 0.000000000
13.019976058 + 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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