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Simplifying M2 = 10 + -12M Solving M2 = 10 + -12M Solving for variable 'M'. Reorder the terms: -10 + 12M + M2 = 10 + -12M + -10 + 12M Reorder the terms: -10 + 12M + M2 = 10 + -10 + -12M + 12M Combine like terms: 10 + -10 = 0 -10 + 12M + M2 = 0 + -12M + 12M -10 + 12M + M2 = -12M + 12M Combine like terms: -12M + 12M = 0 -10 + 12M + M2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 12M + 10 + M2 = 0 + 10 Reorder the terms: -10 + 10 + 12M + M2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 12M + M2 = 0 + 10 12M + M2 = 0 + 10 Combine like terms: 0 + 10 = 10 12M + M2 = 10 The M term is 12M. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12M + 36 + M2 = 10 + 36 Reorder the terms: 36 + 12M + M2 = 10 + 36 Combine like terms: 10 + 36 = 46 36 + 12M + M2 = 46 Factor a perfect square on the left side: (M + 6)(M + 6) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (M + 6) equal to 6.782329983 and -6.782329983.Subproblem 1
M + 6 = 6.782329983 Simplifying M + 6 = 6.782329983 Reorder the terms: 6 + M = 6.782329983 Solving 6 + M = 6.782329983 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + M = 6.782329983 + -6 Combine like terms: 6 + -6 = 0 0 + M = 6.782329983 + -6 M = 6.782329983 + -6 Combine like terms: 6.782329983 + -6 = 0.782329983 M = 0.782329983 Simplifying M = 0.782329983Subproblem 2
M + 6 = -6.782329983 Simplifying M + 6 = -6.782329983 Reorder the terms: 6 + M = -6.782329983 Solving 6 + M = -6.782329983 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + M = -6.782329983 + -6 Combine like terms: 6 + -6 = 0 0 + M = -6.782329983 + -6 M = -6.782329983 + -6 Combine like terms: -6.782329983 + -6 = -12.782329983 M = -12.782329983 Simplifying M = -12.782329983Solution
The solution to the problem is based on the solutions from the subproblems. M = {0.782329983, -12.782329983}
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