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Simplifying m2 + 20m + 27 = 0 Reorder the terms: 27 + 20m + m2 = 0 Solving 27 + 20m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + 20m + -27 + m2 = 0 + -27 Reorder the terms: 27 + -27 + 20m + m2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 20m + m2 = 0 + -27 20m + m2 = 0 + -27 Combine like terms: 0 + -27 = -27 20m + m2 = -27 The m term is 20m. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20m + 100 + m2 = -27 + 100 Reorder the terms: 100 + 20m + m2 = -27 + 100 Combine like terms: -27 + 100 = 73 100 + 20m + m2 = 73 Factor a perfect square on the left side: (m + 10)(m + 10) = 73 Calculate the square root of the right side: 8.544003745 Break this problem into two subproblems by setting (m + 10) equal to 8.544003745 and -8.544003745.Subproblem 1
m + 10 = 8.544003745 Simplifying m + 10 = 8.544003745 Reorder the terms: 10 + m = 8.544003745 Solving 10 + m = 8.544003745 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + m = 8.544003745 + -10 Combine like terms: 10 + -10 = 0 0 + m = 8.544003745 + -10 m = 8.544003745 + -10 Combine like terms: 8.544003745 + -10 = -1.455996255 m = -1.455996255 Simplifying m = -1.455996255Subproblem 2
m + 10 = -8.544003745 Simplifying m + 10 = -8.544003745 Reorder the terms: 10 + m = -8.544003745 Solving 10 + m = -8.544003745 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + m = -8.544003745 + -10 Combine like terms: 10 + -10 = 0 0 + m = -8.544003745 + -10 m = -8.544003745 + -10 Combine like terms: -8.544003745 + -10 = -18.544003745 m = -18.544003745 Simplifying m = -18.544003745Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.455996255, -18.544003745}
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