x^10-7x^9+11x^8=0

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Solution for x^10-7x^9+11x^8=0 equation:


Simplifying
x10 + -7x9 + 11x8 = 0

Reorder the terms:
11x8 + -7x9 + x10 = 0

Solving
11x8 + -7x9 + x10 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x8'.
x8(11 + -7x + x2) = 0

Subproblem 1

Set the factor 'x8' equal to zero and attempt to solve: Simplifying x8 = 0 Solving x8 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x8 = 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 '(11 + -7x + x2)' equal to zero and attempt to solve: Simplifying 11 + -7x + x2 = 0 Solving 11 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -7x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -7x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -7x + x2 = 0 + -11 -7x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -7x + x2 = -11 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 = -11 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -11 + 12.25 Combine like terms: -11 + 12.25 = 1.25 12.25 + -7x + x2 = 1.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -3.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -3.5 = 1.118033989 Simplifying x + -3.5 = 1.118033989 Reorder the terms: -3.5 + x = 1.118033989 Solving -3.5 + x = 1.118033989 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 = 1.118033989 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.118033989 + 3.5 x = 1.118033989 + 3.5 Combine like terms: 1.118033989 + 3.5 = 4.618033989 x = 4.618033989 Simplifying x = 4.618033989

Subproblem 2

x + -3.5 = -1.118033989 Simplifying x + -3.5 = -1.118033989 Reorder the terms: -3.5 + x = -1.118033989 Solving -3.5 + x = -1.118033989 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 = -1.118033989 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.118033989 + 3.5 x = -1.118033989 + 3.5 Combine like terms: -1.118033989 + 3.5 = 2.381966011 x = 2.381966011 Simplifying x = 2.381966011

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.618033989, 2.381966011}

Solution

x = {4.618033989, 2.381966011}

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