25x^4+7x^2-144=0

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Solution for 25x^4+7x^2-144=0 equation: 


Simplifying
25x4 + 7x2 + -144 = 0

Reorder the terms:
-144 + 7x2 + 25x4 = 0

Solving
-144 + 7x2 + 25x4 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
-5.76 + 0.28x2 + x4 = 0

Move the constant term to the right:

Add '5.76' to each side of the equation.
-5.76 + 0.28x2 + 5.76 + x4 = 0 + 5.76

Reorder the terms:
-5.76 + 5.76 + 0.28x2 + x4 = 0 + 5.76

Combine like terms: -5.76 + 5.76 = 0.00
0.00 + 0.28x2 + x4 = 0 + 5.76
0.28x2 + x4 = 0 + 5.76

Combine like terms: 0 + 5.76 = 5.76
0.28x2 + x4 = 5.76

The x term is 0.28x2.  Take half its coefficient (0.14).
Square it (0.0196) and add it to both sides.

Add '0.0196' to each side of the equation.
0.28x2 + 0.0196 + x4 = 5.76 + 0.0196

Reorder the terms:
0.0196 + 0.28x2 + x4 = 5.76 + 0.0196

Combine like terms: 5.76 + 0.0196 = 5.7796
0.0196 + 0.28x2 + x4 = 5.7796

Factor a perfect square on the left side:
(x2 + 0.14)(x2 + 0.14) = 5.7796

Calculate the square root of the right side: 2.404079866

Break this problem into two subproblems by setting 
(x2 + 0.14) equal to 2.404079866 and -2.404079866.


Subproblem 1
x2 + 0.14 = 2.404079866

Simplifying
x2 + 0.14 = 2.404079866

Reorder the terms:
0.14 + x2 = 2.404079866

Solving
0.14 + x2 = 2.404079866

Solving for variable 'x'.

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

Add '-0.14' to each side of the equation.
0.14 + -0.14 + x2 = 2.404079866 + -0.14

Combine like terms: 0.14 + -0.14 = 0.00
0.00 + x2 = 2.404079866 + -0.14
x2 = 2.404079866 + -0.14

Combine like terms: 2.404079866 + -0.14 = 2.264079866
x2 = 2.264079866

Simplifying
x2 = 2.264079866

Take the square root of each side:
x = {-1.504685969, 1.504685969}


Subproblem 2
x2 + 0.14 = -2.404079866

Simplifying
x2 + 0.14 = -2.404079866

Reorder the terms:
0.14 + x2 = -2.404079866

Solving
0.14 + x2 = -2.404079866

Solving for variable 'x'.

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

Add '-0.14' to each side of the equation.
0.14 + -0.14 + x2 = -2.404079866 + -0.14

Combine like terms: 0.14 + -0.14 = 0.00
0.00 + x2 = -2.404079866 + -0.14
x2 = -2.404079866 + -0.14

Combine like terms: -2.404079866 + -0.14 = -2.544079866
x2 = -2.544079866

Simplifying
x2 = -2.544079866

Reorder the terms:
2.544079866 + x2 = -2.544079866 + 2.544079866

Combine like terms: -2.544079866 + 2.544079866 = 0.000000000
2.544079866 + 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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