21x^7+24x^5-6x^3=

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Solution for 21x^7+24x^5-6x^3= equation: 


Simplifying
21x7 + 24x5 + -6x3 = 0

Reorder the terms:
-6x3 + 24x5 + 21x7 = 0

Solving
-6x3 + 24x5 + 21x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x3'.
3x3(-2 + 8x2 + 7x4) = 0

Ignore the factor 3.

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 '(-2 + 8x2 + 7x4)' equal to zero and attempt to solve:

Simplifying
-2 + 8x2 + 7x4 = 0

Solving
-2 + 8x2 + 7x4 = 0

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

Divide each side by '7'.
-0.2857142857 + 1.142857143x2 + x4 = 0

Move the constant term to the right:

Add '0.2857142857' to each side of the equation.
-0.2857142857 + 1.142857143x2 + 0.2857142857 + x4 = 0 + 0.2857142857

Reorder the terms:
-0.2857142857 + 0.2857142857 + 1.142857143x2 + x4 = 0 + 0.2857142857

Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000
0.0000000000 + 1.142857143x2 + x4 = 0 + 0.2857142857
1.142857143x2 + x4 = 0 + 0.2857142857

Combine like terms: 0 + 0.2857142857 = 0.2857142857
1.142857143x2 + x4 = 0.2857142857

The x term is 1.142857143x2.  Take half its coefficient (0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
1.142857143x2 + 0.3265306123 + x4 = 0.2857142857 + 0.3265306123

Reorder the terms:
0.3265306123 + 1.142857143x2 + x4 = 0.2857142857 + 0.3265306123

Combine like terms: 0.2857142857 + 0.3265306123 = 0.612244898
0.3265306123 + 1.142857143x2 + x4 = 0.612244898

Factor a perfect square on the left side:
(x2 + 0.5714285715)(x2 + 0.5714285715) = 0.612244898

Calculate the square root of the right side: 0.782460796

Break this problem into two subproblems by setting 
(x2 + 0.5714285715) equal to 0.782460796 and -0.782460796.


Subproblem 1
x2 + 0.5714285715 = 0.782460796

Simplifying
x2 + 0.5714285715 = 0.782460796

Reorder the terms:
0.5714285715 + x2 = 0.782460796

Solving
0.5714285715 + x2 = 0.782460796

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x2 = 0.782460796 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x2 = 0.782460796 + -0.5714285715
x2 = 0.782460796 + -0.5714285715

Combine like terms: 0.782460796 + -0.5714285715 = 0.2110322245
x2 = 0.2110322245

Simplifying
x2 = 0.2110322245

Take the square root of each side:
x = {-0.459382438, 0.459382438}


Subproblem 2
x2 + 0.5714285715 = -0.782460796

Simplifying
x2 + 0.5714285715 = -0.782460796

Reorder the terms:
0.5714285715 + x2 = -0.782460796

Solving
0.5714285715 + x2 = -0.782460796

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x2 = -0.782460796 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x2 = -0.782460796 + -0.5714285715
x2 = -0.782460796 + -0.5714285715

Combine like terms: -0.782460796 + -0.5714285715 = -1.3538893675
x2 = -1.3538893675

Simplifying
x2 = -1.3538893675

Reorder the terms:
1.3538893675 + x2 = -1.3538893675 + 1.3538893675

Combine like terms: -1.3538893675 + 1.3538893675 = 0.0000000000
1.3538893675 + x2 = 0.0000000000

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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