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Simplifying M2 + 7M = 4 Reorder the terms: 7M + M2 = 4 Solving 7M + M2 = 4 Solving for variable 'M'. Reorder the terms: -4 + 7M + M2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 7M + M2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 7M + 4 + M2 = 0 + 4 Reorder the terms: -4 + 4 + 7M + M2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7M + M2 = 0 + 4 7M + M2 = 0 + 4 Combine like terms: 0 + 4 = 4 7M + M2 = 4 The M term is 7M. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7M + 12.25 + M2 = 4 + 12.25 Reorder the terms: 12.25 + 7M + M2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + 7M + M2 = 16.25 Factor a perfect square on the left side: (M + 3.5)(M + 3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (M + 3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
M + 3.5 = 4.031128874 Simplifying M + 3.5 = 4.031128874 Reorder the terms: 3.5 + M = 4.031128874 Solving 3.5 + M = 4.031128874 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + M = 4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + M = 4.031128874 + -3.5 M = 4.031128874 + -3.5 Combine like terms: 4.031128874 + -3.5 = 0.531128874 M = 0.531128874 Simplifying M = 0.531128874Subproblem 2
M + 3.5 = -4.031128874 Simplifying M + 3.5 = -4.031128874 Reorder the terms: 3.5 + M = -4.031128874 Solving 3.5 + M = -4.031128874 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + M = -4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + M = -4.031128874 + -3.5 M = -4.031128874 + -3.5 Combine like terms: -4.031128874 + -3.5 = -7.531128874 M = -7.531128874 Simplifying M = -7.531128874Solution
The solution to the problem is based on the solutions from the subproblems. M = {0.531128874, -7.531128874}
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