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Simplifying m2 + 6m + -38 = -2 Reorder the terms: -38 + 6m + m2 = -2 Solving -38 + 6m + m2 = -2 Solving for variable 'm'. Reorder the terms: -38 + 2 + 6m + m2 = -2 + 2 Combine like terms: -38 + 2 = -36 -36 + 6m + m2 = -2 + 2 Combine like terms: -2 + 2 = 0 -36 + 6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 6m + 36 + m2 = 0 + 36 Reorder the terms: -36 + 36 + 6m + m2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 6m + m2 = 0 + 36 6m + m2 = 0 + 36 Combine like terms: 0 + 36 = 36 6m + m2 = 36 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 = 36 + 9 Reorder the terms: 9 + 6m + m2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + 6m + m2 = 45 Factor a perfect square on the left side: (m + 3)(m + 3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (m + 3) equal to 6.708203933 and -6.708203933.Subproblem 1
m + 3 = 6.708203933 Simplifying m + 3 = 6.708203933 Reorder the terms: 3 + m = 6.708203933 Solving 3 + m = 6.708203933 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 = 6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + m = 6.708203933 + -3 m = 6.708203933 + -3 Combine like terms: 6.708203933 + -3 = 3.708203933 m = 3.708203933 Simplifying m = 3.708203933Subproblem 2
m + 3 = -6.708203933 Simplifying m + 3 = -6.708203933 Reorder the terms: 3 + m = -6.708203933 Solving 3 + m = -6.708203933 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 = -6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + m = -6.708203933 + -3 m = -6.708203933 + -3 Combine like terms: -6.708203933 + -3 = -9.708203933 m = -9.708203933 Simplifying m = -9.708203933Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.708203933, -9.708203933}
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