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Simplifying 5m5 + -80m3 + 80m = 0 Reorder the terms: 80m + -80m3 + 5m5 = 0 Solving 80m + -80m3 + 5m5 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '5m'. 5m(16 + -16m2 + m4) = 0 Ignore the factor 5.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 '(16 + -16m2 + m4)' equal to zero and attempt to solve: Simplifying 16 + -16m2 + m4 = 0 Solving 16 + -16m2 + m4 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -16m2 + -16 + m4 = 0 + -16 Reorder the terms: 16 + -16 + -16m2 + m4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -16m2 + m4 = 0 + -16 -16m2 + m4 = 0 + -16 Combine like terms: 0 + -16 = -16 -16m2 + m4 = -16 The m term is -16m2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16m2 + 64 + m4 = -16 + 64 Reorder the terms: 64 + -16m2 + m4 = -16 + 64 Combine like terms: -16 + 64 = 48 64 + -16m2 + m4 = 48 Factor a perfect square on the left side: (m2 + -8)(m2 + -8) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (m2 + -8) equal to 6.92820323 and -6.92820323.Subproblem 1
m2 + -8 = 6.92820323 Simplifying m2 + -8 = 6.92820323 Reorder the terms: -8 + m2 = 6.92820323 Solving -8 + m2 = 6.92820323 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + m2 = 6.92820323 + 8 Combine like terms: -8 + 8 = 0 0 + m2 = 6.92820323 + 8 m2 = 6.92820323 + 8 Combine like terms: 6.92820323 + 8 = 14.92820323 m2 = 14.92820323 Simplifying m2 = 14.92820323 Take the square root of each side: m = {-3.863703305, 3.863703305}Subproblem 2
m2 + -8 = -6.92820323 Simplifying m2 + -8 = -6.92820323 Reorder the terms: -8 + m2 = -6.92820323 Solving -8 + m2 = -6.92820323 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + m2 = -6.92820323 + 8 Combine like terms: -8 + 8 = 0 0 + m2 = -6.92820323 + 8 m2 = -6.92820323 + 8 Combine like terms: -6.92820323 + 8 = 1.07179677 m2 = 1.07179677 Simplifying m2 = 1.07179677 Take the square root of each side: m = {-1.035276181, 1.035276181}Solution
The solution to the problem is based on the solutions from the subproblems. m = {-3.863703305, 3.863703305, -1.035276181, 1.035276181}Solution
m = {0, -3.863703305, 3.863703305, -1.035276181, 1.035276181}
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