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Simplifying m4 + 7m3 + m2 = 0 Reorder the terms: m2 + 7m3 + m4 = 0 Solving m2 + 7m3 + m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm2'. m2(1 + 7m + 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 '(1 + 7m + m2)' equal to zero and attempt to solve: Simplifying 1 + 7m + m2 = 0 Solving 1 + 7m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 7m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + 7m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 7m + m2 = 0 + -1 7m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 7m + m2 = -1 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = -1 + 12.25 Reorder the terms: 12.25 + 7m + m2 = -1 + 12.25 Combine like terms: -1 + 12.25 = 11.25 12.25 + 7m + m2 = 11.25 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (m + 3.5) equal to 3.354101966 and -3.354101966.Subproblem 1
m + 3.5 = 3.354101966 Simplifying m + 3.5 = 3.354101966 Reorder the terms: 3.5 + m = 3.354101966 Solving 3.5 + m = 3.354101966 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 3.354101966 + -3.5 m = 3.354101966 + -3.5 Combine like terms: 3.354101966 + -3.5 = -0.145898034 m = -0.145898034 Simplifying m = -0.145898034Subproblem 2
m + 3.5 = -3.354101966 Simplifying m + 3.5 = -3.354101966 Reorder the terms: 3.5 + m = -3.354101966 Solving 3.5 + m = -3.354101966 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -3.354101966 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -3.354101966 + -3.5 m = -3.354101966 + -3.5 Combine like terms: -3.354101966 + -3.5 = -6.854101966 m = -6.854101966 Simplifying m = -6.854101966Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.145898034, -6.854101966}Solution
m = {0, -0.145898034, -6.854101966}
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