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Simplifying 5m2 + 10m + 2 = 0 Reorder the terms: 2 + 10m + 5m2 = 0 Solving 2 + 10m + 5m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 2m + m2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 2m + -0.4 + m2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 2m + m2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 2m + m2 = 0 + -0.4 2m + m2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 2m + m2 = -0.4 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 = -0.4 + 1 Reorder the terms: 1 + 2m + m2 = -0.4 + 1 Combine like terms: -0.4 + 1 = 0.6 1 + 2m + m2 = 0.6 Factor a perfect square on the left side: (m + 1)(m + 1) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (m + 1) equal to 0.774596669 and -0.774596669.Subproblem 1
m + 1 = 0.774596669 Simplifying m + 1 = 0.774596669 Reorder the terms: 1 + m = 0.774596669 Solving 1 + m = 0.774596669 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 = 0.774596669 + -1 Combine like terms: 1 + -1 = 0 0 + m = 0.774596669 + -1 m = 0.774596669 + -1 Combine like terms: 0.774596669 + -1 = -0.225403331 m = -0.225403331 Simplifying m = -0.225403331Subproblem 2
m + 1 = -0.774596669 Simplifying m + 1 = -0.774596669 Reorder the terms: 1 + m = -0.774596669 Solving 1 + m = -0.774596669 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 = -0.774596669 + -1 Combine like terms: 1 + -1 = 0 0 + m = -0.774596669 + -1 m = -0.774596669 + -1 Combine like terms: -0.774596669 + -1 = -1.774596669 m = -1.774596669 Simplifying m = -1.774596669Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.225403331, -1.774596669}
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