7x^5+5x^4=x^3

Solution for 7x^5+5x^4=x^3 equation:

Simplifying
7x5 + 5x4 = x3

Reorder the terms:
5x4 + 7x5 = x3

Solving
5x4 + 7x5 = x3

Solving for variable 'x'.

Reorder the terms:
-1x3 + 5x4 + 7x5 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-1x3 + 5x4 + 7x5 = 0

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-1 + 5x + 7x2) = 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 '(-1 + 5x + 7x2)' equal to zero and attempt to solve:

Simplifying
-1 + 5x + 7x2 = 0

Solving
-1 + 5x + 7x2 = 0

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

Divide each side by '7'.
-0.1428571429 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.7142857143x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 0.7142857143x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 0.7142857143x + x2 = 0 + 0.1428571429
0.7142857143x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
0.7142857143x + x2 = 0.1428571429

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = 0.1428571429 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = 0.1428571429 + 0.1275510204

Combine like terms: 0.1428571429 + 0.1275510204 = 0.2704081633
0.1275510204 + 0.7142857143x + x2 = 0.2704081633

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 0.2704081633

Calculate the square root of the right side: 0.520007849

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 0.520007849 and -0.520007849.

Subproblem 1
x + 0.3571428572 = 0.520007849

Simplifying
x + 0.3571428572 = 0.520007849

Reorder the terms:
0.3571428572 + x = 0.520007849

Solving
0.3571428572 + x = 0.520007849

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = 0.520007849 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = 0.520007849 + -0.3571428572
x = 0.520007849 + -0.3571428572

Combine like terms: 0.520007849 + -0.3571428572 = 0.1628649918
x = 0.1628649918

Simplifying
x = 0.1628649918

Subproblem 2
x + 0.3571428572 = -0.520007849

Simplifying
x + 0.3571428572 = -0.520007849

Reorder the terms:
0.3571428572 + x = -0.520007849

Solving
0.3571428572 + x = -0.520007849

Solving for variable 'x'.

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

Add '-0.3571428572' to each side of the equation.
0.3571428572 + -0.3571428572 + x = -0.520007849 + -0.3571428572

Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000
0.0000000000 + x = -0.520007849 + -0.3571428572
x = -0.520007849 + -0.3571428572

Combine like terms: -0.520007849 + -0.3571428572 = -0.8771507062
x = -0.8771507062

Simplifying
x = -0.8771507062

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1628649918, -0.8771507062}
Solution
x = {0.1628649918, -0.8771507062}