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Simplifying x5 + -16x4 + 16x3 = 0 Reorder the terms: 16x3 + -16x4 + x5 = 0 Solving 16x3 + -16x4 + x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x3'. x3(16 + -16x + x2) = 0Subproblem 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 '(16 + -16x + x2)' equal to zero and attempt to solve: Simplifying 16 + -16x + x2 = 0 Solving 16 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -16x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -16x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -16x + x2 = 0 + -16 -16x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -16x + x2 = -16 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -16 + 64 Reorder the terms: 64 + -16x + x2 = -16 + 64 Combine like terms: -16 + 64 = 48 64 + -16x + x2 = 48 Factor a perfect square on the left side: (x + -8)(x + -8) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -8) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -8 = 6.92820323 Simplifying x + -8 = 6.92820323 Reorder the terms: -8 + x = 6.92820323 Solving -8 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 6.92820323 + 8 Combine like terms: -8 + 8 = 0 0 + x = 6.92820323 + 8 x = 6.92820323 + 8 Combine like terms: 6.92820323 + 8 = 14.92820323 x = 14.92820323 Simplifying x = 14.92820323Subproblem 2
x + -8 = -6.92820323 Simplifying x + -8 = -6.92820323 Reorder the terms: -8 + x = -6.92820323 Solving -8 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -6.92820323 + 8 Combine like terms: -8 + 8 = 0 0 + x = -6.92820323 + 8 x = -6.92820323 + 8 Combine like terms: -6.92820323 + 8 = 1.07179677 x = 1.07179677 Simplifying x = 1.07179677Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.92820323, 1.07179677}Solution
x = {14.92820323, 1.07179677}
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