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Simplifying m2 + -6m + -36 = 0 Reorder the terms: -36 + -6m + m2 = 0 Solving -36 + -6m + m2 = 0 Solving for variable 'm'. 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 = 9.708203933 m = 9.708203933 Simplifying m = 9.708203933Subproblem 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 = -3.708203933 m = -3.708203933 Simplifying m = -3.708203933Solution
The solution to the problem is based on the solutions from the subproblems. m = {9.708203933, -3.708203933}
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