25x^6-60x^3-36=0

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Solution for 25x^6-60x^3-36=0 equation:


Simplifying
25x6 + -60x3 + -36 = 0

Reorder the terms:
-36 + -60x3 + 25x6 = 0

Solving
-36 + -60x3 + 25x6 = 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'.
-1.44 + -2.4x3 + x6 = 0

Move the constant term to the right:

Add '1.44' to each side of the equation.
-1.44 + -2.4x3 + 1.44 + x6 = 0 + 1.44

Reorder the terms:
-1.44 + 1.44 + -2.4x3 + x6 = 0 + 1.44

Combine like terms: -1.44 + 1.44 = 0.00
0.00 + -2.4x3 + x6 = 0 + 1.44
-2.4x3 + x6 = 0 + 1.44

Combine like terms: 0 + 1.44 = 1.44
-2.4x3 + x6 = 1.44

The x term is -2.4x3.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x3 + 1.44 + x6 = 1.44 + 1.44

Reorder the terms:
1.44 + -2.4x3 + x6 = 1.44 + 1.44

Combine like terms: 1.44 + 1.44 = 2.88
1.44 + -2.4x3 + x6 = 2.88

Factor a perfect square on the left side:
(x3 + -1.2)(x3 + -1.2) = 2.88

Calculate the square root of the right side: 1.697056275

Break this problem into two subproblems by setting 
(x3 + -1.2) equal to 1.697056275 and -1.697056275.

Subproblem 1

x3 + -1.2 = 1.697056275 Simplifying x3 + -1.2 = 1.697056275 Reorder the terms: -1.2 + x3 = 1.697056275 Solving -1.2 + x3 = 1.697056275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x3 = 1.697056275 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x3 = 1.697056275 + 1.2 x3 = 1.697056275 + 1.2 Combine like terms: 1.697056275 + 1.2 = 2.897056275 x3 = 2.897056275 Simplifying x3 = 2.897056275 Reorder the terms: -2.897056275 + x3 = 2.897056275 + -2.897056275 Combine like terms: 2.897056275 + -2.897056275 = 0.000000000 -2.897056275 + x3 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

Subproblem 2

x3 + -1.2 = -1.697056275 Simplifying x3 + -1.2 = -1.697056275 Reorder the terms: -1.2 + x3 = -1.697056275 Solving -1.2 + x3 = -1.697056275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x3 = -1.697056275 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x3 = -1.697056275 + 1.2 x3 = -1.697056275 + 1.2 Combine like terms: -1.697056275 + 1.2 = -0.497056275 x3 = -0.497056275 Simplifying x3 = -0.497056275 Reorder the terms: 0.497056275 + x3 = -0.497056275 + 0.497056275 Combine like terms: -0.497056275 + 0.497056275 = 0.000000000 0.497056275 + x3 = 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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