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Simplifying m2 + -1m = 115 Reorder the terms: -1m + m2 = 115 Solving -1m + m2 = 115 Solving for variable 'm'. Reorder the terms: -115 + -1m + m2 = 115 + -115 Combine like terms: 115 + -115 = 0 -115 + -1m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '115' to each side of the equation. -115 + -1m + 115 + m2 = 0 + 115 Reorder the terms: -115 + 115 + -1m + m2 = 0 + 115 Combine like terms: -115 + 115 = 0 0 + -1m + m2 = 0 + 115 -1m + m2 = 0 + 115 Combine like terms: 0 + 115 = 115 -1m + m2 = 115 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. -1m + 0.25 + m2 = 115 + 0.25 Reorder the terms: 0.25 + -1m + m2 = 115 + 0.25 Combine like terms: 115 + 0.25 = 115.25 0.25 + -1m + m2 = 115.25 Factor a perfect square on the left side: (m + -0.5)(m + -0.5) = 115.25 Calculate the square root of the right side: 10.735455277 Break this problem into two subproblems by setting (m + -0.5) equal to 10.735455277 and -10.735455277.Subproblem 1
m + -0.5 = 10.735455277 Simplifying m + -0.5 = 10.735455277 Reorder the terms: -0.5 + m = 10.735455277 Solving -0.5 + m = 10.735455277 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 = 10.735455277 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 10.735455277 + 0.5 m = 10.735455277 + 0.5 Combine like terms: 10.735455277 + 0.5 = 11.235455277 m = 11.235455277 Simplifying m = 11.235455277Subproblem 2
m + -0.5 = -10.735455277 Simplifying m + -0.5 = -10.735455277 Reorder the terms: -0.5 + m = -10.735455277 Solving -0.5 + m = -10.735455277 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 = -10.735455277 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -10.735455277 + 0.5 m = -10.735455277 + 0.5 Combine like terms: -10.735455277 + 0.5 = -10.235455277 m = -10.235455277 Simplifying m = -10.235455277Solution
The solution to the problem is based on the solutions from the subproblems. m = {11.235455277, -10.235455277}
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