4x^4+21x^2-144=0

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Solution for 4x^4+21x^2-144=0 equation: 


Simplifying
4x4 + 21x2 + -144 = 0

Reorder the terms:
-144 + 21x2 + 4x4 = 0

Solving
-144 + 21x2 + 4x4 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-36 + 5.25x2 + x4 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 5.25x2 + 36 + x4 = 0 + 36

Reorder the terms:
-36 + 36 + 5.25x2 + x4 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 5.25x2 + x4 = 0 + 36
5.25x2 + x4 = 0 + 36

Combine like terms: 0 + 36 = 36
5.25x2 + x4 = 36

The x term is 5.25x2.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25x2 + 6.890625 + x4 = 36 + 6.890625

Reorder the terms:
6.890625 + 5.25x2 + x4 = 36 + 6.890625

Combine like terms: 36 + 6.890625 = 42.890625
6.890625 + 5.25x2 + x4 = 42.890625

Factor a perfect square on the left side:
(x2 + 2.625)(x2 + 2.625) = 42.890625

Calculate the square root of the right side: 6.549093449

Break this problem into two subproblems by setting 
(x2 + 2.625) equal to 6.549093449 and -6.549093449.


Subproblem 1
x2 + 2.625 = 6.549093449

Simplifying
x2 + 2.625 = 6.549093449

Reorder the terms:
2.625 + x2 = 6.549093449

Solving
2.625 + x2 = 6.549093449

Solving for variable 'x'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x2 = 6.549093449 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x2 = 6.549093449 + -2.625
x2 = 6.549093449 + -2.625

Combine like terms: 6.549093449 + -2.625 = 3.924093449
x2 = 3.924093449

Simplifying
x2 = 3.924093449

Take the square root of each side:
x = {-1.98093247, 1.98093247}


Subproblem 2
x2 + 2.625 = -6.549093449

Simplifying
x2 + 2.625 = -6.549093449

Reorder the terms:
2.625 + x2 = -6.549093449

Solving
2.625 + x2 = -6.549093449

Solving for variable 'x'.

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

Add '-2.625' to each side of the equation.
2.625 + -2.625 + x2 = -6.549093449 + -2.625

Combine like terms: 2.625 + -2.625 = 0.000
0.000 + x2 = -6.549093449 + -2.625
x2 = -6.549093449 + -2.625

Combine like terms: -6.549093449 + -2.625 = -9.174093449
x2 = -9.174093449

Simplifying
x2 = -9.174093449

Reorder the terms:
9.174093449 + x2 = -9.174093449 + 9.174093449

Combine like terms: -9.174093449 + 9.174093449 = 0.000000000
9.174093449 + 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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