x^4-28x^6=-48x^5

Solution for x^4-28x^6=-48x^5 equation:

Simplifying
x4 + -28x6 = -48x5

Solving
x4 + -28x6 = -48x5

Solving for variable 'x'.

Reorder the terms:
x4 + 48x5 + -28x6 = -48x5 + 48x5

Combine like terms: -48x5 + 48x5 = 0
x4 + 48x5 + -28x6 = 0

Factor out the Greatest Common Factor (GCF), 'x4'.
x4(1 + 48x + -28x2) = 0

Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve:

Simplifying
x4 = 0

Solving
x4 = 0

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

Simplifying
x4 = 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 + 48x + -28x2)' equal to zero and attempt to solve:

Simplifying
1 + 48x + -28x2 = 0

Solving
1 + 48x + -28x2 = 0

Begin completing the square.  Divide all terms by
-28 the coefficient of the squared term: 

Divide each side by '-28'.
-0.03571428571 + -1.714285714x + x2 = 0

Move the constant term to the right:

Add '0.03571428571' to each side of the equation.
-0.03571428571 + -1.714285714x + 0.03571428571 + x2 = 0 + 0.03571428571

Reorder the terms:
-0.03571428571 + 0.03571428571 + -1.714285714x + x2 = 0 + 0.03571428571

Combine like terms: -0.03571428571 + 0.03571428571 = 0.00000000000
0.00000000000 + -1.714285714x + x2 = 0 + 0.03571428571
-1.714285714x + x2 = 0 + 0.03571428571

Combine like terms: 0 + 0.03571428571 = 0.03571428571
-1.714285714x + x2 = 0.03571428571

The x term is -1.714285714x.  Take half its coefficient (-0.857142857).
Square it (0.7346938773) and add it to both sides.

Add '0.7346938773' to each side of the equation.
-1.714285714x + 0.7346938773 + x2 = 0.03571428571 + 0.7346938773

Reorder the terms:
0.7346938773 + -1.714285714x + x2 = 0.03571428571 + 0.7346938773

Combine like terms: 0.03571428571 + 0.7346938773 = 0.77040816301
0.7346938773 + -1.714285714x + x2 = 0.77040816301

Factor a perfect square on the left side:
(x + -0.857142857)(x + -0.857142857) = 0.77040816301

Calculate the square root of the right side: 0.87772898

Break this problem into two subproblems by setting 
(x + -0.857142857) equal to 0.87772898 and -0.87772898.

Subproblem 1
x + -0.857142857 = 0.87772898

Simplifying
x + -0.857142857 = 0.87772898

Reorder the terms:
-0.857142857 + x = 0.87772898

Solving
-0.857142857 + x = 0.87772898

Solving for variable 'x'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + x = 0.87772898 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = 0.87772898 + 0.857142857
x = 0.87772898 + 0.857142857

Combine like terms: 0.87772898 + 0.857142857 = 1.734871837
x = 1.734871837

Simplifying
x = 1.734871837

Subproblem 2
x + -0.857142857 = -0.87772898

Simplifying
x + -0.857142857 = -0.87772898

Reorder the terms:
-0.857142857 + x = -0.87772898

Solving
-0.857142857 + x = -0.87772898

Solving for variable 'x'.

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

Add '0.857142857' to each side of the equation.
-0.857142857 + 0.857142857 + x = -0.87772898 + 0.857142857

Combine like terms: -0.857142857 + 0.857142857 = 0.000000000
0.000000000 + x = -0.87772898 + 0.857142857
x = -0.87772898 + 0.857142857

Combine like terms: -0.87772898 + 0.857142857 = -0.020586123
x = -0.020586123

Simplifying
x = -0.020586123

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.734871837, -0.020586123}
Solution
x = {1.734871837, -0.020586123}