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Simplifying (m4) + (m3) + (m2) = 0 m4 + (m3) + (m2) = 0 m4 + m3 + (m2) = 0 m4 + m3 + m2 = 0 Reorder the terms: m2 + m3 + m4 = 0 Solving m2 + m3 + m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm2'. m2(1 + 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 '(1 + m + m2)' equal to zero and attempt to solve: Simplifying 1 + m + m2 = 0 Solving 1 + m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + m + -1 + m2 = 0 + -1 Reorder the terms: 1 + -1 + m + m2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + m + m2 = 0 + -1 m + m2 = 0 + -1 Combine like terms: 0 + -1 = -1 m + m2 = -1 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 = -1 + 0.25 Reorder the terms: 0.25 + m + m2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + m + m2 = -0.75 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
m = {0}
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