4x^4-7x^2-144=0

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Solution for 4x^4-7x^2-144=0 equation: 


Simplifying
4x4 + -7x2 + -144 = 0

Reorder the terms:
-144 + -7x2 + 4x4 = 0

Solving
-144 + -7x2 + 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 + -1.75x2 + x4 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -1.75x2 + 36 + x4 = 0 + 36

Reorder the terms:
-36 + 36 + -1.75x2 + x4 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -1.75x2 + x4 = 0 + 36
-1.75x2 + x4 = 0 + 36

Combine like terms: 0 + 36 = 36
-1.75x2 + x4 = 36

The x term is -1.75x2.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x2 + 0.765625 + x4 = 36 + 0.765625

Reorder the terms:
0.765625 + -1.75x2 + x4 = 36 + 0.765625

Combine like terms: 36 + 0.765625 = 36.765625
0.765625 + -1.75x2 + x4 = 36.765625

Factor a perfect square on the left side:
(x2 + -0.875)(x2 + -0.875) = 36.765625

Calculate the square root of the right side: 6.063466418

Break this problem into two subproblems by setting 
(x2 + -0.875) equal to 6.063466418 and -6.063466418.


Subproblem 1
x2 + -0.875 = 6.063466418

Simplifying
x2 + -0.875 = 6.063466418

Reorder the terms:
-0.875 + x2 = 6.063466418

Solving
-0.875 + x2 = 6.063466418

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x2 = 6.063466418 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x2 = 6.063466418 + 0.875
x2 = 6.063466418 + 0.875

Combine like terms: 6.063466418 + 0.875 = 6.938466418
x2 = 6.938466418

Simplifying
x2 = 6.938466418

Take the square root of each side:
x = {-2.634096888, 2.634096888}


Subproblem 2
x2 + -0.875 = -6.063466418

Simplifying
x2 + -0.875 = -6.063466418

Reorder the terms:
-0.875 + x2 = -6.063466418

Solving
-0.875 + x2 = -6.063466418

Solving for variable 'x'.

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

Add '0.875' to each side of the equation.
-0.875 + 0.875 + x2 = -6.063466418 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + x2 = -6.063466418 + 0.875
x2 = -6.063466418 + 0.875

Combine like terms: -6.063466418 + 0.875 = -5.188466418
x2 = -5.188466418

Simplifying
x2 = -5.188466418

Reorder the terms:
5.188466418 + x2 = -5.188466418 + 5.188466418

Combine like terms: -5.188466418 + 5.188466418 = 0.000000000
5.188466418 + 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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