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Simplifying x3 + -16x2 + -4x = 0 Reorder the terms: -4x + -16x2 + x3 = 0 Solving -4x + -16x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + -16x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-4 + -16x + x2)' equal to zero and attempt to solve: Simplifying -4 + -16x + x2 = 0 Solving -4 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -16x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -16x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -16x + x2 = 0 + 4 -16x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -16x + x2 = 4 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 = 4 + 64 Reorder the terms: 64 + -16x + x2 = 4 + 64 Combine like terms: 4 + 64 = 68 64 + -16x + x2 = 68 Factor a perfect square on the left side: (x + -8)(x + -8) = 68 Calculate the square root of the right side: 8.246211251 Break this problem into two subproblems by setting (x + -8) equal to 8.246211251 and -8.246211251.Subproblem 1
x + -8 = 8.246211251 Simplifying x + -8 = 8.246211251 Reorder the terms: -8 + x = 8.246211251 Solving -8 + x = 8.246211251 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 = 8.246211251 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.246211251 + 8 x = 8.246211251 + 8 Combine like terms: 8.246211251 + 8 = 16.246211251 x = 16.246211251 Simplifying x = 16.246211251Subproblem 2
x + -8 = -8.246211251 Simplifying x + -8 = -8.246211251 Reorder the terms: -8 + x = -8.246211251 Solving -8 + x = -8.246211251 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 = -8.246211251 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.246211251 + 8 x = -8.246211251 + 8 Combine like terms: -8.246211251 + 8 = -0.246211251 x = -0.246211251 Simplifying x = -0.246211251Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.246211251, -0.246211251}Solution
x = {0, 16.246211251, -0.246211251}
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