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Simplifying (m + 3) * m = 26 Reorder the terms: (3 + m) * m = 26 Reorder the terms for easier multiplication: m(3 + m) = 26 (3 * m + m * m) = 26 (3m + m2) = 26 Solving 3m + m2 = 26 Solving for variable 'm'. Reorder the terms: -26 + 3m + m2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 3m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 3m + 26 + m2 = 0 + 26 Reorder the terms: -26 + 26 + 3m + m2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 3m + m2 = 0 + 26 3m + m2 = 0 + 26 Combine like terms: 0 + 26 = 26 3m + m2 = 26 The m term is 3m. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3m + 2.25 + m2 = 26 + 2.25 Reorder the terms: 2.25 + 3m + m2 = 26 + 2.25 Combine like terms: 26 + 2.25 = 28.25 2.25 + 3m + m2 = 28.25 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (m + 1.5) equal to 5.315072906 and -5.315072906.Subproblem 1
m + 1.5 = 5.315072906 Simplifying m + 1.5 = 5.315072906 Reorder the terms: 1.5 + m = 5.315072906 Solving 1.5 + m = 5.315072906 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 5.315072906 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 5.315072906 + -1.5 m = 5.315072906 + -1.5 Combine like terms: 5.315072906 + -1.5 = 3.815072906 m = 3.815072906 Simplifying m = 3.815072906Subproblem 2
m + 1.5 = -5.315072906 Simplifying m + 1.5 = -5.315072906 Reorder the terms: 1.5 + m = -5.315072906 Solving 1.5 + m = -5.315072906 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -5.315072906 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -5.315072906 + -1.5 m = -5.315072906 + -1.5 Combine like terms: -5.315072906 + -1.5 = -6.815072906 m = -6.815072906 Simplifying m = -6.815072906Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.815072906, -6.815072906}
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