4x^7-28x^6-80x^5=

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Solution for 4x^7-28x^6-80x^5= equation:


Simplifying
4x7 + -28x6 + -80x5 = 0

Reorder the terms:
-80x5 + -28x6 + 4x7 = 0

Solving
-80x5 + -28x6 + 4x7 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x5'.
4x5(-20 + -7x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 'x5' equal to zero and attempt to solve: Simplifying x5 = 0 Solving x5 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x5 = 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 '(-20 + -7x + x2)' equal to zero and attempt to solve: Simplifying -20 + -7x + x2 = 0 Solving -20 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -7x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -7x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -7x + x2 = 0 + 20 -7x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -7x + x2 = 20 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 20 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 20 + 12.25 Combine like terms: 20 + 12.25 = 32.25 12.25 + -7x + x2 = 32.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (x + -3.5) equal to 5.678908346 and -5.678908346.

Subproblem 1

x + -3.5 = 5.678908346 Simplifying x + -3.5 = 5.678908346 Reorder the terms: -3.5 + x = 5.678908346 Solving -3.5 + x = 5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.678908346 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.678908346 + 3.5 x = 5.678908346 + 3.5 Combine like terms: 5.678908346 + 3.5 = 9.178908346 x = 9.178908346 Simplifying x = 9.178908346

Subproblem 2

x + -3.5 = -5.678908346 Simplifying x + -3.5 = -5.678908346 Reorder the terms: -3.5 + x = -5.678908346 Solving -3.5 + x = -5.678908346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.678908346 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.678908346 + 3.5 x = -5.678908346 + 3.5 Combine like terms: -5.678908346 + 3.5 = -2.178908346 x = -2.178908346 Simplifying x = -2.178908346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.178908346, -2.178908346}

Solution

x = {9.178908346, -2.178908346}

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