56x^7-42x^5-5x^3=

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Solution for 56x^7-42x^5-5x^3= equation: 


Simplifying
56x7 + -42x5 + -5x3 = 0

Reorder the terms:
-5x3 + -42x5 + 56x7 = 0

Solving
-5x3 + -42x5 + 56x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-5 + -42x2 + 56x4) = 0


Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(-5 + -42x2 + 56x4)' equal to zero and attempt to solve:

Simplifying
-5 + -42x2 + 56x4 = 0

Solving
-5 + -42x2 + 56x4 = 0

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

Divide each side by '56'.
-0.08928571429 + -0.75x2 + x4 = 0

Move the constant term to the right:

Add '0.08928571429' to each side of the equation.
-0.08928571429 + -0.75x2 + 0.08928571429 + x4 = 0 + 0.08928571429

Reorder the terms:
-0.08928571429 + 0.08928571429 + -0.75x2 + x4 = 0 + 0.08928571429

Combine like terms: -0.08928571429 + 0.08928571429 = 0.00000000000
0.00000000000 + -0.75x2 + x4 = 0 + 0.08928571429
-0.75x2 + x4 = 0 + 0.08928571429

Combine like terms: 0 + 0.08928571429 = 0.08928571429
-0.75x2 + x4 = 0.08928571429

The x term is -0.75x2.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x2 + 0.140625 + x4 = 0.08928571429 + 0.140625

Reorder the terms:
0.140625 + -0.75x2 + x4 = 0.08928571429 + 0.140625

Combine like terms: 0.08928571429 + 0.140625 = 0.22991071429
0.140625 + -0.75x2 + x4 = 0.22991071429

Factor a perfect square on the left side:
(x2 + -0.375)(x2 + -0.375) = 0.22991071429

Calculate the square root of the right side: 0.479490057

Break this problem into two subproblems by setting 
(x2 + -0.375) equal to 0.479490057 and -0.479490057.


Subproblem 1
x2 + -0.375 = 0.479490057

Simplifying
x2 + -0.375 = 0.479490057

Reorder the terms:
-0.375 + x2 = 0.479490057

Solving
-0.375 + x2 = 0.479490057

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x2 = 0.479490057 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x2 = 0.479490057 + 0.375
x2 = 0.479490057 + 0.375

Combine like terms: 0.479490057 + 0.375 = 0.854490057
x2 = 0.854490057

Simplifying
x2 = 0.854490057

Take the square root of each side:
x = {-0.924386314, 0.924386314}


Subproblem 2
x2 + -0.375 = -0.479490057

Simplifying
x2 + -0.375 = -0.479490057

Reorder the terms:
-0.375 + x2 = -0.479490057

Solving
-0.375 + x2 = -0.479490057

Solving for variable 'x'.

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

Add '0.375' to each side of the equation.
-0.375 + 0.375 + x2 = -0.479490057 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + x2 = -0.479490057 + 0.375
x2 = -0.479490057 + 0.375

Combine like terms: -0.479490057 + 0.375 = -0.104490057
x2 = -0.104490057

Simplifying
x2 = -0.104490057

Reorder the terms:
0.104490057 + x2 = -0.104490057 + 0.104490057

Combine like terms: -0.104490057 + 0.104490057 = 0.000000000
0.104490057 + 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.

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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