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

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


Simplifying
x2 + -1x4 + 24x2 + 144 = 4

Reorder the terms:
144 + x2 + 24x2 + -1x4 = 4

Combine like terms: x2 + 24x2 = 25x2
144 + 25x2 + -1x4 = 4

Solving
144 + 25x2 + -1x4 = 4

Solving for variable 'x'.

Reorder the terms:
144 + -4 + 25x2 + -1x4 = 4 + -4

Combine like terms: 144 + -4 = 140
140 + 25x2 + -1x4 = 4 + -4

Combine like terms: 4 + -4 = 0
140 + 25x2 + -1x4 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-140 + -25x2 + x4 = 0

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + -25x2 + 140 + x4 = 0 + 140

Reorder the terms:
-140 + 140 + -25x2 + x4 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + -25x2 + x4 = 0 + 140
-25x2 + x4 = 0 + 140

Combine like terms: 0 + 140 = 140
-25x2 + x4 = 140

The x term is -25x2.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x2 + 156.25 + x4 = 140 + 156.25

Reorder the terms:
156.25 + -25x2 + x4 = 140 + 156.25

Combine like terms: 140 + 156.25 = 296.25
156.25 + -25x2 + x4 = 296.25

Factor a perfect square on the left side:
(x2 + -12.5)(x2 + -12.5) = 296.25

Calculate the square root of the right side: 17.211914478

Break this problem into two subproblems by setting 
(x2 + -12.5) equal to 17.211914478 and -17.211914478.


Subproblem 1
x2 + -12.5 = 17.211914478

Simplifying
x2 + -12.5 = 17.211914478

Reorder the terms:
-12.5 + x2 = 17.211914478

Solving
-12.5 + x2 = 17.211914478

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x2 = 17.211914478 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x2 = 17.211914478 + 12.5
x2 = 17.211914478 + 12.5

Combine like terms: 17.211914478 + 12.5 = 29.711914478
x2 = 29.711914478

Simplifying
x2 = 29.711914478

Take the square root of each side:
x = {-5.450863645, 5.450863645}


Subproblem 2
x2 + -12.5 = -17.211914478

Simplifying
x2 + -12.5 = -17.211914478

Reorder the terms:
-12.5 + x2 = -17.211914478

Solving
-12.5 + x2 = -17.211914478

Solving for variable 'x'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + x2 = -17.211914478 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + x2 = -17.211914478 + 12.5
x2 = -17.211914478 + 12.5

Combine like terms: -17.211914478 + 12.5 = -4.711914478
x2 = -4.711914478

Simplifying
x2 = -4.711914478

Reorder the terms:
4.711914478 + x2 = -4.711914478 + 4.711914478

Combine like terms: -4.711914478 + 4.711914478 = 0.000000000
4.711914478 + 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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