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Simplifying m2 + m = 28 Reorder the terms: m + m2 = 28 Solving m + m2 = 28 Solving for variable 'm'. Reorder the terms: -28 + m + m2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + m + 28 + m2 = 0 + 28 Reorder the terms: -28 + 28 + m + m2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + m + m2 = 0 + 28 m + m2 = 0 + 28 Combine like terms: 0 + 28 = 28 m + m2 = 28 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. m + 0.25 + m2 = 28 + 0.25 Reorder the terms: 0.25 + m + m2 = 28 + 0.25 Combine like terms: 28 + 0.25 = 28.25 0.25 + m + m2 = 28.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (m + 0.5) equal to 5.315072906 and -5.315072906.Subproblem 1
m + 0.5 = 5.315072906 Simplifying m + 0.5 = 5.315072906 Reorder the terms: 0.5 + m = 5.315072906 Solving 0.5 + m = 5.315072906 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 5.315072906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 5.315072906 + -0.5 m = 5.315072906 + -0.5 Combine like terms: 5.315072906 + -0.5 = 4.815072906 m = 4.815072906 Simplifying m = 4.815072906Subproblem 2
m + 0.5 = -5.315072906 Simplifying m + 0.5 = -5.315072906 Reorder the terms: 0.5 + m = -5.315072906 Solving 0.5 + m = -5.315072906 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -5.315072906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -5.315072906 + -0.5 m = -5.315072906 + -0.5 Combine like terms: -5.315072906 + -0.5 = -5.815072906 m = -5.815072906 Simplifying m = -5.815072906Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.815072906, -5.815072906}
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