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

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


Simplifying
x5 + -1x4 + -5x3 = 0

Reorder the terms:
-5x3 + -1x4 + x5 = 0

Solving
-5x3 + -1x4 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x3'.
x3(-5 + -1x + 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 '(-5 + -1x + x2)' equal to zero and attempt to solve: Simplifying -5 + -1x + x2 = 0 Solving -5 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -1x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -1x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x + x2 = 0 + 5 -1x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1x + x2 = 5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1x + x2 = 5.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + -0.5 = 2.291287847 Simplifying x + -0.5 = 2.291287847 Reorder the terms: -0.5 + x = 2.291287847 Solving -0.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.291287847 + 0.5 x = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 x = 2.791287847 Simplifying x = 2.791287847

Subproblem 2

x + -0.5 = -2.291287847 Simplifying x + -0.5 = -2.291287847 Reorder the terms: -0.5 + x = -2.291287847 Solving -0.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.291287847 + 0.5 x = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 x = -1.791287847 Simplifying x = -1.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.791287847, -1.791287847}

Solution

x = {2.791287847, -1.791287847}

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