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Simplifying (5m2 + -29m + -6) + (5m + 1) = m + -6 Reorder the terms: (-6 + -29m + 5m2) + (5m + 1) = m + -6 Remove parenthesis around (-6 + -29m + 5m2) -6 + -29m + 5m2 + (5m + 1) = m + -6 Reorder the terms: -6 + -29m + 5m2 + (1 + 5m) = m + -6 Remove parenthesis around (1 + 5m) -6 + -29m + 5m2 + 1 + 5m = m + -6 Reorder the terms: -6 + 1 + -29m + 5m + 5m2 = m + -6 Combine like terms: -6 + 1 = -5 -5 + -29m + 5m + 5m2 = m + -6 Combine like terms: -29m + 5m = -24m -5 + -24m + 5m2 = m + -6 Reorder the terms: -5 + -24m + 5m2 = -6 + m Solving -5 + -24m + 5m2 = -6 + m Solving for variable 'm'. Reorder the terms: -5 + 6 + -24m + -1m + 5m2 = -6 + m + 6 + -1m Combine like terms: -5 + 6 = 1 1 + -24m + -1m + 5m2 = -6 + m + 6 + -1m Combine like terms: -24m + -1m = -25m 1 + -25m + 5m2 = -6 + m + 6 + -1m Reorder the terms: 1 + -25m + 5m2 = -6 + 6 + m + -1m Combine like terms: -6 + 6 = 0 1 + -25m + 5m2 = 0 + m + -1m 1 + -25m + 5m2 = m + -1m Combine like terms: m + -1m = 0 1 + -25m + 5m2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -5m + m2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -5m + -0.2 + m2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -5m + m2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -5m + m2 = 0 + -0.2 -5m + m2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -5m + m2 = -0.2 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 = -0.2 + 6.25 Reorder the terms: 6.25 + -5m + m2 = -0.2 + 6.25 Combine like terms: -0.2 + 6.25 = 6.05 6.25 + -5m + m2 = 6.05 Factor a perfect square on the left side: (m + -2.5)(m + -2.5) = 6.05 Calculate the square root of the right side: 2.459674775 Break this problem into two subproblems by setting (m + -2.5) equal to 2.459674775 and -2.459674775.Subproblem 1
m + -2.5 = 2.459674775 Simplifying m + -2.5 = 2.459674775 Reorder the terms: -2.5 + m = 2.459674775 Solving -2.5 + m = 2.459674775 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 = 2.459674775 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = 2.459674775 + 2.5 m = 2.459674775 + 2.5 Combine like terms: 2.459674775 + 2.5 = 4.959674775 m = 4.959674775 Simplifying m = 4.959674775Subproblem 2
m + -2.5 = -2.459674775 Simplifying m + -2.5 = -2.459674775 Reorder the terms: -2.5 + m = -2.459674775 Solving -2.5 + m = -2.459674775 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 = -2.459674775 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + m = -2.459674775 + 2.5 m = -2.459674775 + 2.5 Combine like terms: -2.459674775 + 2.5 = 0.040325225 m = 0.040325225 Simplifying m = 0.040325225Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.959674775, 0.040325225}
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