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Simplifying m3 + 2m2 + -5m = 0 Reorder the terms: -5m + 2m2 + m3 = 0 Solving -5m + 2m2 + m3 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm'. m(-5 + 2m + m2) = 0Subproblem 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 '(-5 + 2m + m2)' equal to zero and attempt to solve: Simplifying -5 + 2m + m2 = 0 Solving -5 + 2m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2m + 5 + m2 = 0 + 5 Reorder the terms: -5 + 5 + 2m + m2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2m + m2 = 0 + 5 2m + m2 = 0 + 5 Combine like terms: 0 + 5 = 5 2m + m2 = 5 The m term is 2m. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2m + 1 + m2 = 5 + 1 Reorder the terms: 1 + 2m + m2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2m + m2 = 6 Factor a perfect square on the left side: (m + 1)(m + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (m + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
m + 1 = 2.449489743 Simplifying m + 1 = 2.449489743 Reorder the terms: 1 + m = 2.449489743 Solving 1 + m = 2.449489743 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + m = 2.449489743 + -1 m = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 m = 1.449489743 Simplifying m = 1.449489743Subproblem 2
m + 1 = -2.449489743 Simplifying m + 1 = -2.449489743 Reorder the terms: 1 + m = -2.449489743 Solving 1 + m = -2.449489743 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + m = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + m = -2.449489743 + -1 m = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 m = -3.449489743 Simplifying m = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.449489743, -3.449489743}Solution
m = {0, 1.449489743, -3.449489743}
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