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Simplifying m4 + m3 + -40m2 = 0 Reorder the terms: -40m2 + m3 + m4 = 0 Solving -40m2 + m3 + m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm2'. m2(-40 + m + m2) = 0Subproblem 1
Set the factor 'm2' equal to zero and attempt to solve: Simplifying m2 = 0 Solving m2 = 0 Move all terms containing m to the left, all other terms to the right. Simplifying m2 = 0 Take the square root of each side: m = {0}Subproblem 2
Set the factor '(-40 + m + m2)' equal to zero and attempt to solve: Simplifying -40 + m + m2 = 0 Solving -40 + m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + m + 40 + m2 = 0 + 40 Reorder the terms: -40 + 40 + m + m2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + m + m2 = 0 + 40 m + m2 = 0 + 40 Combine like terms: 0 + 40 = 40 m + m2 = 40 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. m + 0.25 + m2 = 40 + 0.25 Reorder the terms: 0.25 + m + m2 = 40 + 0.25 Combine like terms: 40 + 0.25 = 40.25 0.25 + m + m2 = 40.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (m + 0.5) equal to 6.34428877 and -6.34428877.Subproblem 1
m + 0.5 = 6.34428877 Simplifying m + 0.5 = 6.34428877 Reorder the terms: 0.5 + m = 6.34428877 Solving 0.5 + m = 6.34428877 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 6.34428877 + -0.5 m = 6.34428877 + -0.5 Combine like terms: 6.34428877 + -0.5 = 5.84428877 m = 5.84428877 Simplifying m = 5.84428877Subproblem 2
m + 0.5 = -6.34428877 Simplifying m + 0.5 = -6.34428877 Reorder the terms: 0.5 + m = -6.34428877 Solving 0.5 + m = -6.34428877 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -6.34428877 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -6.34428877 + -0.5 m = -6.34428877 + -0.5 Combine like terms: -6.34428877 + -0.5 = -6.84428877 m = -6.84428877 Simplifying m = -6.84428877Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.84428877, -6.84428877}Solution
m = {0, 5.84428877, -6.84428877}
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