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Simplifying m(m + 1) = 200 Reorder the terms: m(1 + m) = 200 (1 * m + m * m) = 200 (1m + m2) = 200 Solving 1m + m2 = 200 Solving for variable 'm'. Reorder the terms: -200 + 1m + m2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 1m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 1m + 200 + m2 = 0 + 200 Reorder the terms: -200 + 200 + 1m + m2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 1m + m2 = 0 + 200 1m + m2 = 0 + 200 Combine like terms: 0 + 200 = 200 1m + m2 = 200 The m term is 1m. 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 = 200 + 0.25 Reorder the terms: 0.25 + m + m2 = 200 + 0.25 Combine like terms: 200 + 0.25 = 200.25 0.25 + m + m2 = 200.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (m + 0.5) equal to 14.150971698 and -14.150971698.Subproblem 1
m + 0.5 = 14.150971698 Simplifying m + 0.5 = 14.150971698 Reorder the terms: 0.5 + m = 14.150971698 Solving 0.5 + m = 14.150971698 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 = 14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 14.150971698 + -0.5 m = 14.150971698 + -0.5 Combine like terms: 14.150971698 + -0.5 = 13.650971698 m = 13.650971698 Simplifying m = 13.650971698Subproblem 2
m + 0.5 = -14.150971698 Simplifying m + 0.5 = -14.150971698 Reorder the terms: 0.5 + m = -14.150971698 Solving 0.5 + m = -14.150971698 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 = -14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -14.150971698 + -0.5 m = -14.150971698 + -0.5 Combine like terms: -14.150971698 + -0.5 = -14.650971698 m = -14.650971698 Simplifying m = -14.650971698Solution
The solution to the problem is based on the solutions from the subproblems. m = {13.650971698, -14.650971698}
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