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Simplifying 32m3 + -16m2 + -2m = 0 Reorder the terms: -2m + -16m2 + 32m3 = 0 Solving -2m + -16m2 + 32m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '2m'. 2m(-1 + -8m + 16m2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'm' equal to zero and attempt to solve: Simplifying m = 0 Solving m = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m = 0Subproblem 2
Set the factor '(-1 + -8m + 16m2)' equal to zero and attempt to solve: Simplifying -1 + -8m + 16m2 = 0 Solving -1 + -8m + 16m2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -0.5m + m2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.5m + 0.0625 + m2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.5m + m2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.5m + m2 = 0 + 0.0625 -0.5m + m2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.5m + m2 = 0.0625 The m term is -0.5m. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5m + 0.0625 + m2 = 0.0625 + 0.0625 Reorder the terms: 0.0625 + -0.5m + m2 = 0.0625 + 0.0625 Combine like terms: 0.0625 + 0.0625 = 0.125 0.0625 + -0.5m + m2 = 0.125 Factor a perfect square on the left side: (m + -0.25)(m + -0.25) = 0.125 Calculate the square root of the right side: 0.353553391 Break this problem into two subproblems by setting (m + -0.25) equal to 0.353553391 and -0.353553391.Subproblem 1
m + -0.25 = 0.353553391 Simplifying m + -0.25 = 0.353553391 Reorder the terms: -0.25 + m = 0.353553391 Solving -0.25 + m = 0.353553391 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + m = 0.353553391 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = 0.353553391 + 0.25 m = 0.353553391 + 0.25 Combine like terms: 0.353553391 + 0.25 = 0.603553391 m = 0.603553391 Simplifying m = 0.603553391Subproblem 2
m + -0.25 = -0.353553391 Simplifying m + -0.25 = -0.353553391 Reorder the terms: -0.25 + m = -0.353553391 Solving -0.25 + m = -0.353553391 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + m = -0.353553391 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + m = -0.353553391 + 0.25 m = -0.353553391 + 0.25 Combine like terms: -0.353553391 + 0.25 = -0.103553391 m = -0.103553391 Simplifying m = -0.103553391Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.603553391, -0.103553391}Solution
m = {0, 0.603553391, -0.103553391}
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