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Simplifying m2 + -1m + -50 = 0 Reorder the terms: -50 + -1m + m2 = 0 Solving -50 + -1m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + -1m + 50 + m2 = 0 + 50 Reorder the terms: -50 + 50 + -1m + m2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -1m + m2 = 0 + 50 -1m + m2 = 0 + 50 Combine like terms: 0 + 50 = 50 -1m + m2 = 50 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 = 50 + 0.25 Reorder the terms: 0.25 + -1m + m2 = 50 + 0.25 Combine like terms: 50 + 0.25 = 50.25 0.25 + -1m + m2 = 50.25 Factor a perfect square on the left side: (m + -0.5)(m + -0.5) = 50.25 Calculate the square root of the right side: 7.088723439 Break this problem into two subproblems by setting (m + -0.5) equal to 7.088723439 and -7.088723439.Subproblem 1
m + -0.5 = 7.088723439 Simplifying m + -0.5 = 7.088723439 Reorder the terms: -0.5 + m = 7.088723439 Solving -0.5 + m = 7.088723439 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 = 7.088723439 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = 7.088723439 + 0.5 m = 7.088723439 + 0.5 Combine like terms: 7.088723439 + 0.5 = 7.588723439 m = 7.588723439 Simplifying m = 7.588723439Subproblem 2
m + -0.5 = -7.088723439 Simplifying m + -0.5 = -7.088723439 Reorder the terms: -0.5 + m = -7.088723439 Solving -0.5 + m = -7.088723439 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 = -7.088723439 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + m = -7.088723439 + 0.5 m = -7.088723439 + 0.5 Combine like terms: -7.088723439 + 0.5 = -6.588723439 m = -6.588723439 Simplifying m = -6.588723439Solution
The solution to the problem is based on the solutions from the subproblems. m = {7.588723439, -6.588723439}
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