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Simplifying M2 + 10M + -21 = 2 Reorder the terms: -21 + 10M + M2 = 2 Solving -21 + 10M + M2 = 2 Solving for variable 'M'. Reorder the terms: -21 + -2 + 10M + M2 = 2 + -2 Combine like terms: -21 + -2 = -23 -23 + 10M + M2 = 2 + -2 Combine like terms: 2 + -2 = 0 -23 + 10M + M2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 10M + 23 + M2 = 0 + 23 Reorder the terms: -23 + 23 + 10M + M2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 10M + M2 = 0 + 23 10M + M2 = 0 + 23 Combine like terms: 0 + 23 = 23 10M + M2 = 23 The M term is 10M. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10M + 25 + M2 = 23 + 25 Reorder the terms: 25 + 10M + M2 = 23 + 25 Combine like terms: 23 + 25 = 48 25 + 10M + M2 = 48 Factor a perfect square on the left side: (M + 5)(M + 5) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (M + 5) equal to 6.92820323 and -6.92820323.Subproblem 1
M + 5 = 6.92820323 Simplifying M + 5 = 6.92820323 Reorder the terms: 5 + M = 6.92820323 Solving 5 + M = 6.92820323 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + M = 6.92820323 + -5 Combine like terms: 5 + -5 = 0 0 + M = 6.92820323 + -5 M = 6.92820323 + -5 Combine like terms: 6.92820323 + -5 = 1.92820323 M = 1.92820323 Simplifying M = 1.92820323Subproblem 2
M + 5 = -6.92820323 Simplifying M + 5 = -6.92820323 Reorder the terms: 5 + M = -6.92820323 Solving 5 + M = -6.92820323 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + M = -6.92820323 + -5 Combine like terms: 5 + -5 = 0 0 + M = -6.92820323 + -5 M = -6.92820323 + -5 Combine like terms: -6.92820323 + -5 = -11.92820323 M = -11.92820323 Simplifying M = -11.92820323Solution
The solution to the problem is based on the solutions from the subproblems. M = {1.92820323, -11.92820323}
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