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Simplifying (m * m) + -2m + -6 = 0 Multiply m * m (m2) + -2m + -6 = 0 m2 + -2m + -6 = 0 Reorder the terms: -6 + -2m + m2 = 0 Solving -6 + -2m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -2m + 6 + m2 = 0 + 6 Reorder the terms: -6 + 6 + -2m + m2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -2m + m2 = 0 + 6 -2m + m2 = 0 + 6 Combine like terms: 0 + 6 = 6 -2m + m2 = 6 The m term is -2m. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2m + 1 + m2 = 6 + 1 Reorder the terms: 1 + -2m + m2 = 6 + 1 Combine like terms: 6 + 1 = 7 1 + -2m + m2 = 7 Factor a perfect square on the left side: (m + -1)(m + -1) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (m + -1) equal to 2.645751311 and -2.645751311.Subproblem 1
m + -1 = 2.645751311 Simplifying m + -1 = 2.645751311 Reorder the terms: -1 + m = 2.645751311 Solving -1 + m = 2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = 2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + m = 2.645751311 + 1 m = 2.645751311 + 1 Combine like terms: 2.645751311 + 1 = 3.645751311 m = 3.645751311 Simplifying m = 3.645751311Subproblem 2
m + -1 = -2.645751311 Simplifying m + -1 = -2.645751311 Reorder the terms: -1 + m = -2.645751311 Solving -1 + m = -2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + m = -2.645751311 + 1 Combine like terms: -1 + 1 = 0 0 + m = -2.645751311 + 1 m = -2.645751311 + 1 Combine like terms: -2.645751311 + 1 = -1.645751311 m = -1.645751311 Simplifying m = -1.645751311Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.645751311, -1.645751311}
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