x^5-14x^4-48x^3=0

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Solution for x^5-14x^4-48x^3=0 equation: 


Simplifying
x5 + -14x4 + -48x3 = 0

Reorder the terms:
-48x3 + -14x4 + x5 = 0

Solving
-48x3 + -14x4 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-48 + -14x + x2) = 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 '(-48 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
-48 + -14x + x2 = 0

Solving
-48 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + -14x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + -14x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + -14x + x2 = 0 + 48
-14x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
-14x + x2 = 48

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 48 + 49

Reorder the terms:
49 + -14x + x2 = 48 + 49

Combine like terms: 48 + 49 = 97
49 + -14x + x2 = 97

Factor a perfect square on the left side:
(x + -7)(x + -7) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + -7) equal to 9.848857802 and -9.848857802.


Subproblem 1
x + -7 = 9.848857802

Simplifying
x + -7 = 9.848857802

Reorder the terms:
-7 + x = 9.848857802

Solving
-7 + x = 9.848857802

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 9.848857802 + 7

Combine like terms: -7 + 7 = 0
0 + x = 9.848857802 + 7
x = 9.848857802 + 7

Combine like terms: 9.848857802 + 7 = 16.848857802
x = 16.848857802

Simplifying
x = 16.848857802


Subproblem 2
x + -7 = -9.848857802

Simplifying
x + -7 = -9.848857802

Reorder the terms:
-7 + x = -9.848857802

Solving
-7 + x = -9.848857802

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -9.848857802 + 7

Combine like terms: -7 + 7 = 0
0 + x = -9.848857802 + 7
x = -9.848857802 + 7

Combine like terms: -9.848857802 + 7 = -2.848857802
x = -2.848857802

Simplifying
x = -2.848857802


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.848857802, -2.848857802}
Solution
x = {16.848857802, -2.848857802}

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