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Simplifying 4m + 20m + 5 + m2 + 8m + 5m + 5 = 0 Reorder the terms: 5 + 5 + 4m + 20m + 8m + 5m + m2 = 0 Combine like terms: 5 + 5 = 10 10 + 4m + 20m + 8m + 5m + m2 = 0 Combine like terms: 4m + 20m = 24m 10 + 24m + 8m + 5m + m2 = 0 Combine like terms: 24m + 8m = 32m 10 + 32m + 5m + m2 = 0 Combine like terms: 32m + 5m = 37m 10 + 37m + m2 = 0 Solving 10 + 37m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 37m + -10 + m2 = 0 + -10 Reorder the terms: 10 + -10 + 37m + m2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 37m + m2 = 0 + -10 37m + m2 = 0 + -10 Combine like terms: 0 + -10 = -10 37m + m2 = -10 The m term is 37m. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37m + 342.25 + m2 = -10 + 342.25 Reorder the terms: 342.25 + 37m + m2 = -10 + 342.25 Combine like terms: -10 + 342.25 = 332.25 342.25 + 37m + m2 = 332.25 Factor a perfect square on the left side: (m + 18.5)(m + 18.5) = 332.25 Calculate the square root of the right side: 18.227726134 Break this problem into two subproblems by setting (m + 18.5) equal to 18.227726134 and -18.227726134.Subproblem 1
m + 18.5 = 18.227726134 Simplifying m + 18.5 = 18.227726134 Reorder the terms: 18.5 + m = 18.227726134 Solving 18.5 + m = 18.227726134 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + m = 18.227726134 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + m = 18.227726134 + -18.5 m = 18.227726134 + -18.5 Combine like terms: 18.227726134 + -18.5 = -0.272273866 m = -0.272273866 Simplifying m = -0.272273866Subproblem 2
m + 18.5 = -18.227726134 Simplifying m + 18.5 = -18.227726134 Reorder the terms: 18.5 + m = -18.227726134 Solving 18.5 + m = -18.227726134 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + m = -18.227726134 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + m = -18.227726134 + -18.5 m = -18.227726134 + -18.5 Combine like terms: -18.227726134 + -18.5 = -36.727726134 m = -36.727726134 Simplifying m = -36.727726134Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.272273866, -36.727726134}
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