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Simplifying m2 + -6m + -73 = 60 Reorder the terms: -73 + -6m + m2 = 60 Solving -73 + -6m + m2 = 60 Solving for variable 'm'. Reorder the terms: -73 + -60 + -6m + m2 = 60 + -60 Combine like terms: -73 + -60 = -133 -133 + -6m + m2 = 60 + -60 Combine like terms: 60 + -60 = 0 -133 + -6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '133' to each side of the equation. -133 + -6m + 133 + m2 = 0 + 133 Reorder the terms: -133 + 133 + -6m + m2 = 0 + 133 Combine like terms: -133 + 133 = 0 0 + -6m + m2 = 0 + 133 -6m + m2 = 0 + 133 Combine like terms: 0 + 133 = 133 -6m + m2 = 133 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 = 133 + 9 Reorder the terms: 9 + -6m + m2 = 133 + 9 Combine like terms: 133 + 9 = 142 9 + -6m + m2 = 142 Factor a perfect square on the left side: (m + -3)(m + -3) = 142 Calculate the square root of the right side: 11.916375288 Break this problem into two subproblems by setting (m + -3) equal to 11.916375288 and -11.916375288.Subproblem 1
m + -3 = 11.916375288 Simplifying m + -3 = 11.916375288 Reorder the terms: -3 + m = 11.916375288 Solving -3 + m = 11.916375288 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 = 11.916375288 + 3 Combine like terms: -3 + 3 = 0 0 + m = 11.916375288 + 3 m = 11.916375288 + 3 Combine like terms: 11.916375288 + 3 = 14.916375288 m = 14.916375288 Simplifying m = 14.916375288Subproblem 2
m + -3 = -11.916375288 Simplifying m + -3 = -11.916375288 Reorder the terms: -3 + m = -11.916375288 Solving -3 + m = -11.916375288 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 = -11.916375288 + 3 Combine like terms: -3 + 3 = 0 0 + m = -11.916375288 + 3 m = -11.916375288 + 3 Combine like terms: -11.916375288 + 3 = -8.916375288 m = -8.916375288 Simplifying m = -8.916375288Solution
The solution to the problem is based on the solutions from the subproblems. m = {14.916375288, -8.916375288}
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