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Simplifying m2 + -6m + -73 = 0 Reorder the terms: -73 + -6m + m2 = 0 Solving -73 + -6m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '73' to each side of the equation. -73 + -6m + 73 + m2 = 0 + 73 Reorder the terms: -73 + 73 + -6m + m2 = 0 + 73 Combine like terms: -73 + 73 = 0 0 + -6m + m2 = 0 + 73 -6m + m2 = 0 + 73 Combine like terms: 0 + 73 = 73 -6m + m2 = 73 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 = 73 + 9 Reorder the terms: 9 + -6m + m2 = 73 + 9 Combine like terms: 73 + 9 = 82 9 + -6m + m2 = 82 Factor a perfect square on the left side: (m + -3)(m + -3) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (m + -3) equal to 9.055385138 and -9.055385138.Subproblem 1
m + -3 = 9.055385138 Simplifying m + -3 = 9.055385138 Reorder the terms: -3 + m = 9.055385138 Solving -3 + m = 9.055385138 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 = 9.055385138 + 3 Combine like terms: -3 + 3 = 0 0 + m = 9.055385138 + 3 m = 9.055385138 + 3 Combine like terms: 9.055385138 + 3 = 12.055385138 m = 12.055385138 Simplifying m = 12.055385138Subproblem 2
m + -3 = -9.055385138 Simplifying m + -3 = -9.055385138 Reorder the terms: -3 + m = -9.055385138 Solving -3 + m = -9.055385138 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 = -9.055385138 + 3 Combine like terms: -3 + 3 = 0 0 + m = -9.055385138 + 3 m = -9.055385138 + 3 Combine like terms: -9.055385138 + 3 = -6.055385138 m = -6.055385138 Simplifying m = -6.055385138Solution
The solution to the problem is based on the solutions from the subproblems. m = {12.055385138, -6.055385138}
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