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Simplifying 20m2 + 40m + 4 = 0 Reorder the terms: 4 + 40m + 20m2 = 0 Solving 4 + 40m + 20m2 = 0 Solving for variable 'm'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 10m + 5m2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 10m + 5m2)' equal to zero and attempt to solve: Simplifying 1 + 10m + 5m2 = 0 Solving 1 + 10m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + 2m + m2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 2m + -0.2 + m2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + 2m + m2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 2m + m2 = 0 + -0.2 2m + m2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 2m + m2 = -0.2 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 = -0.2 + 1 Reorder the terms: 1 + 2m + m2 = -0.2 + 1 Combine like terms: -0.2 + 1 = 0.8 1 + 2m + m2 = 0.8 Factor a perfect square on the left side: (m + 1)(m + 1) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (m + 1) equal to 0.894427191 and -0.894427191.Subproblem 1
m + 1 = 0.894427191 Simplifying m + 1 = 0.894427191 Reorder the terms: 1 + m = 0.894427191 Solving 1 + m = 0.894427191 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 = 0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + m = 0.894427191 + -1 m = 0.894427191 + -1 Combine like terms: 0.894427191 + -1 = -0.105572809 m = -0.105572809 Simplifying m = -0.105572809Subproblem 2
m + 1 = -0.894427191 Simplifying m + 1 = -0.894427191 Reorder the terms: 1 + m = -0.894427191 Solving 1 + m = -0.894427191 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 = -0.894427191 + -1 Combine like terms: 1 + -1 = 0 0 + m = -0.894427191 + -1 m = -0.894427191 + -1 Combine like terms: -0.894427191 + -1 = -1.894427191 m = -1.894427191 Simplifying m = -1.894427191Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.105572809, -1.894427191}Solution
m = {-0.105572809, -1.894427191}
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