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Simplifying -5m4 + -5m3 + 5m2 = 0 Reorder the terms: 5m2 + -5m3 + -5m4 = 0 Solving 5m2 + -5m3 + -5m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '5m2'. 5m2(1 + -1m + -1m2) = 0 Ignore the factor 5.Subproblem 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 + -1m + -1m2)' equal to zero and attempt to solve: Simplifying 1 + -1m + -1m2 = 0 Solving 1 + -1m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + m + m2 = 0 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. + 0.25 + m2 = 1 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + m2 = 1 + 0.25 Combine like terms: 1 + 0.25 = 1.25 1.25 + m2 = 1.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (m + 0.5) equal to 1.118033989 and -1.118033989.Subproblem 1
m + 0.5 = 1.118033989 Simplifying m + 0.5 = 1.118033989 Reorder the terms: 0.5 + m = 1.118033989 Solving 0.5 + m = 1.118033989 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 = 1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.118033989 + -0.5 m = 1.118033989 + -0.5 Combine like terms: 1.118033989 + -0.5 = 0.618033989 m = 0.618033989 Simplifying m = 0.618033989Subproblem 2
m + 0.5 = -1.118033989 Simplifying m + 0.5 = -1.118033989 Reorder the terms: 0.5 + m = -1.118033989 Solving 0.5 + m = -1.118033989 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 = -1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.118033989 + -0.5 m = -1.118033989 + -0.5 Combine like terms: -1.118033989 + -0.5 = -1.618033989 m = -1.618033989 Simplifying m = -1.618033989Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.618033989, -1.618033989}Solution
m = {0, 0.618033989, -1.618033989}
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