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Simplifying 5m3 + -1m2 + 4m2 + -1m4 = 0 Reorder the terms: -1m2 + 4m2 + 5m3 + -1m4 = 0 Combine like terms: -1m2 + 4m2 = 3m2 3m2 + 5m3 + -1m4 = 0 Solving 3m2 + 5m3 + -1m4 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), 'm2'. m2(3 + 5m + -1m2) = 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 '(3 + 5m + -1m2)' equal to zero and attempt to solve: Simplifying 3 + 5m + -1m2 = 0 Solving 3 + 5m + -1m2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -5m + m2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -5m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + -5m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5m + m2 = 0 + 3 -5m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5m + m2 = 3 The m term is -5m. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5m + 6.25 + m2 = 3 + 6.25 Reorder the terms: 6.25 + -5m + m2 = 3 + 6.25 Combine like terms: 3 + 6.25 = 9.25 6.25 + -5m + m2 = 9.25 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (m + -2.5) equal to 3.041381265 and -3.041381265.Subproblem 1
m + -2.5 = 3.041381265 Simplifying m + -2.5 = 3.041381265 Reorder the terms: -2.5 + m = 3.041381265 Solving -2.5 + m = 3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = 3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 3.041381265 + 2.5 m = 3.041381265 + 2.5 Combine like terms: 3.041381265 + 2.5 = 5.541381265 m = 5.541381265 Simplifying m = 5.541381265Subproblem 2
m + -2.5 = -3.041381265 Simplifying m + -2.5 = -3.041381265 Reorder the terms: -2.5 + m = -3.041381265 Solving -2.5 + m = -3.041381265 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + m = -3.041381265 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -3.041381265 + 2.5 m = -3.041381265 + 2.5 Combine like terms: -3.041381265 + 2.5 = -0.541381265 m = -0.541381265 Simplifying m = -0.541381265Solution
The solution to the problem is based on the solutions from the subproblems. m = {5.541381265, -0.541381265}Solution
m = {0, 5.541381265, -0.541381265}
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