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Simplifying 7M2 + 12M + 3 = 0 Reorder the terms: 3 + 12M + 7M2 = 0 Solving 3 + 12M + 7M2 = 0 Solving for variable 'M'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.4285714286 + 1.714285714M + M2 = 0 Move the constant term to the right: Add '-0.4285714286' to each side of the equation. 0.4285714286 + 1.714285714M + -0.4285714286 + M2 = 0 + -0.4285714286 Reorder the terms: 0.4285714286 + -0.4285714286 + 1.714285714M + M2 = 0 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + 1.714285714M + M2 = 0 + -0.4285714286 1.714285714M + M2 = 0 + -0.4285714286 Combine like terms: 0 + -0.4285714286 = -0.4285714286 1.714285714M + M2 = -0.4285714286 The M term is 1.714285714M. Take half its coefficient (0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. 1.714285714M + 0.7346938773 + M2 = -0.4285714286 + 0.7346938773 Reorder the terms: 0.7346938773 + 1.714285714M + M2 = -0.4285714286 + 0.7346938773 Combine like terms: -0.4285714286 + 0.7346938773 = 0.3061224487 0.7346938773 + 1.714285714M + M2 = 0.3061224487 Factor a perfect square on the left side: (M + 0.857142857)(M + 0.857142857) = 0.3061224487 Calculate the square root of the right side: 0.553283335 Break this problem into two subproblems by setting (M + 0.857142857) equal to 0.553283335 and -0.553283335.Subproblem 1
M + 0.857142857 = 0.553283335 Simplifying M + 0.857142857 = 0.553283335 Reorder the terms: 0.857142857 + M = 0.553283335 Solving 0.857142857 + M = 0.553283335 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + M = 0.553283335 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + M = 0.553283335 + -0.857142857 M = 0.553283335 + -0.857142857 Combine like terms: 0.553283335 + -0.857142857 = -0.303859522 M = -0.303859522 Simplifying M = -0.303859522Subproblem 2
M + 0.857142857 = -0.553283335 Simplifying M + 0.857142857 = -0.553283335 Reorder the terms: 0.857142857 + M = -0.553283335 Solving 0.857142857 + M = -0.553283335 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-0.857142857' to each side of the equation. 0.857142857 + -0.857142857 + M = -0.553283335 + -0.857142857 Combine like terms: 0.857142857 + -0.857142857 = 0.000000000 0.000000000 + M = -0.553283335 + -0.857142857 M = -0.553283335 + -0.857142857 Combine like terms: -0.553283335 + -0.857142857 = -1.410426192 M = -1.410426192 Simplifying M = -1.410426192Solution
The solution to the problem is based on the solutions from the subproblems. M = {-0.303859522, -1.410426192}
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