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Simplifying x6 + -6x5 + -6x4 = 0 Reorder the terms: -6x4 + -6x5 + x6 = 0 Solving -6x4 + -6x5 + x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x4'. x4(-6 + -6x + x2) = 0Subproblem 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 '(-6 + -6x + x2)' equal to zero and attempt to solve: Simplifying -6 + -6x + x2 = 0 Solving -6 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -6x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -6x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -6x + x2 = 0 + 6 -6x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -6x + x2 = 6 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 6 + 9 Reorder the terms: 9 + -6x + x2 = 6 + 9 Combine like terms: 6 + 9 = 15 9 + -6x + x2 = 15 Factor a perfect square on the left side: (x + -3)(x + -3) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + -3) equal to 3.872983346 and -3.872983346.Subproblem 1
x + -3 = 3.872983346 Simplifying x + -3 = 3.872983346 Reorder the terms: -3 + x = 3.872983346 Solving -3 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.872983346 + 3 x = 3.872983346 + 3 Combine like terms: 3.872983346 + 3 = 6.872983346 x = 6.872983346 Simplifying x = 6.872983346Subproblem 2
x + -3 = -3.872983346 Simplifying x + -3 = -3.872983346 Reorder the terms: -3 + x = -3.872983346 Solving -3 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.872983346 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.872983346 + 3 x = -3.872983346 + 3 Combine like terms: -3.872983346 + 3 = -0.872983346 x = -0.872983346 Simplifying x = -0.872983346Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.872983346, -0.872983346}Solution
x = {6.872983346, -0.872983346}
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