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Simplifying m2 + 6m + -41 = 0 Reorder the terms: -41 + 6m + m2 = 0 Solving -41 + 6m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 6m + 41 + m2 = 0 + 41 Reorder the terms: -41 + 41 + 6m + m2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 6m + m2 = 0 + 41 6m + m2 = 0 + 41 Combine like terms: 0 + 41 = 41 6m + m2 = 41 The m term is 6m. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6m + 9 + m2 = 41 + 9 Reorder the terms: 9 + 6m + m2 = 41 + 9 Combine like terms: 41 + 9 = 50 9 + 6m + m2 = 50 Factor a perfect square on the left side: (m + 3)(m + 3) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (m + 3) equal to 7.071067812 and -7.071067812.Subproblem 1
m + 3 = 7.071067812 Simplifying m + 3 = 7.071067812 Reorder the terms: 3 + m = 7.071067812 Solving 3 + m = 7.071067812 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = 7.071067812 + -3 Combine like terms: 3 + -3 = 0 0 + m = 7.071067812 + -3 m = 7.071067812 + -3 Combine like terms: 7.071067812 + -3 = 4.071067812 m = 4.071067812 Simplifying m = 4.071067812Subproblem 2
m + 3 = -7.071067812 Simplifying m + 3 = -7.071067812 Reorder the terms: 3 + m = -7.071067812 Solving 3 + m = -7.071067812 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = -7.071067812 + -3 Combine like terms: 3 + -3 = 0 0 + m = -7.071067812 + -3 m = -7.071067812 + -3 Combine like terms: -7.071067812 + -3 = -10.071067812 m = -10.071067812 Simplifying m = -10.071067812Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.071067812, -10.071067812}
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