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Simplifying m2 + 13m + 27 = 0 Reorder the terms: 27 + 13m + m2 = 0 Solving 27 + 13m + 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 + 13m + -27 + m2 = 0 + -27 Reorder the terms: 27 + -27 + 13m + m2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + 13m + m2 = 0 + -27 13m + m2 = 0 + -27 Combine like terms: 0 + -27 = -27 13m + m2 = -27 The m term is 13m. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13m + 42.25 + m2 = -27 + 42.25 Reorder the terms: 42.25 + 13m + m2 = -27 + 42.25 Combine like terms: -27 + 42.25 = 15.25 42.25 + 13m + m2 = 15.25 Factor a perfect square on the left side: (m + 6.5)(m + 6.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (m + 6.5) equal to 3.905124838 and -3.905124838.Subproblem 1
m + 6.5 = 3.905124838 Simplifying m + 6.5 = 3.905124838 Reorder the terms: 6.5 + m = 3.905124838 Solving 6.5 + m = 3.905124838 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + m = 3.905124838 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + m = 3.905124838 + -6.5 m = 3.905124838 + -6.5 Combine like terms: 3.905124838 + -6.5 = -2.594875162 m = -2.594875162 Simplifying m = -2.594875162Subproblem 2
m + 6.5 = -3.905124838 Simplifying m + 6.5 = -3.905124838 Reorder the terms: 6.5 + m = -3.905124838 Solving 6.5 + m = -3.905124838 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + m = -3.905124838 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + m = -3.905124838 + -6.5 m = -3.905124838 + -6.5 Combine like terms: -3.905124838 + -6.5 = -10.405124838 m = -10.405124838 Simplifying m = -10.405124838Solution
The solution to the problem is based on the solutions from the subproblems. m = {-2.594875162, -10.405124838}
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