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Simplifying M2 + 8M = 3 Reorder the terms: 8M + M2 = 3 Solving 8M + M2 = 3 Solving for variable 'M'. Reorder the terms: -3 + 8M + M2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 8M + M2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 8M + 3 + M2 = 0 + 3 Reorder the terms: -3 + 3 + 8M + M2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8M + M2 = 0 + 3 8M + M2 = 0 + 3 Combine like terms: 0 + 3 = 3 8M + M2 = 3 The M term is 8M. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8M + 16 + M2 = 3 + 16 Reorder the terms: 16 + 8M + M2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + 8M + M2 = 19 Factor a perfect square on the left side: (M + 4)(M + 4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (M + 4) equal to 4.358898944 and -4.358898944.Subproblem 1
M + 4 = 4.358898944 Simplifying M + 4 = 4.358898944 Reorder the terms: 4 + M = 4.358898944 Solving 4 + M = 4.358898944 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + M = 4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + M = 4.358898944 + -4 M = 4.358898944 + -4 Combine like terms: 4.358898944 + -4 = 0.358898944 M = 0.358898944 Simplifying M = 0.358898944Subproblem 2
M + 4 = -4.358898944 Simplifying M + 4 = -4.358898944 Reorder the terms: 4 + M = -4.358898944 Solving 4 + M = -4.358898944 Solving for variable 'M'. Move all terms containing M to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + M = -4.358898944 + -4 Combine like terms: 4 + -4 = 0 0 + M = -4.358898944 + -4 M = -4.358898944 + -4 Combine like terms: -4.358898944 + -4 = -8.358898944 M = -8.358898944 Simplifying M = -8.358898944Solution
The solution to the problem is based on the solutions from the subproblems. M = {0.358898944, -8.358898944}
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