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Simplifying m2 + m + -294 = 0 Reorder the terms: -294 + m + m2 = 0 Solving -294 + m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '294' to each side of the equation. -294 + m + 294 + m2 = 0 + 294 Reorder the terms: -294 + 294 + m + m2 = 0 + 294 Combine like terms: -294 + 294 = 0 0 + m + m2 = 0 + 294 m + m2 = 0 + 294 Combine like terms: 0 + 294 = 294 m + m2 = 294 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 = 294 + 0.25 Reorder the terms: 0.25 + m + m2 = 294 + 0.25 Combine like terms: 294 + 0.25 = 294.25 0.25 + m + m2 = 294.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 294.25 Calculate the square root of the right side: 17.153716798 Break this problem into two subproblems by setting (m + 0.5) equal to 17.153716798 and -17.153716798.Subproblem 1
m + 0.5 = 17.153716798 Simplifying m + 0.5 = 17.153716798 Reorder the terms: 0.5 + m = 17.153716798 Solving 0.5 + m = 17.153716798 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 = 17.153716798 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 17.153716798 + -0.5 m = 17.153716798 + -0.5 Combine like terms: 17.153716798 + -0.5 = 16.653716798 m = 16.653716798 Simplifying m = 16.653716798Subproblem 2
m + 0.5 = -17.153716798 Simplifying m + 0.5 = -17.153716798 Reorder the terms: 0.5 + m = -17.153716798 Solving 0.5 + m = -17.153716798 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 = -17.153716798 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -17.153716798 + -0.5 m = -17.153716798 + -0.5 Combine like terms: -17.153716798 + -0.5 = -17.653716798 m = -17.653716798 Simplifying m = -17.653716798Solution
The solution to the problem is based on the solutions from the subproblems. m = {16.653716798, -17.653716798}
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