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Simplifying 3m + -6 + (m)(m) + -5m + 1 = 0 Multiply m * m 3m + -6 + m2 + -5m + 1 = 0 Reorder the terms: -6 + 1 + 3m + -5m + m2 = 0 Combine like terms: -6 + 1 = -5 -5 + 3m + -5m + m2 = 0 Combine like terms: 3m + -5m = -2m -5 + -2m + m2 = 0 Solving -5 + -2m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2m + 5 + m2 = 0 + 5 Reorder the terms: -5 + 5 + -2m + m2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2m + m2 = 0 + 5 -2m + m2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2m + m2 = 5 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 = 5 + 1 Reorder the terms: 1 + -2m + m2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2m + m2 = 6 Factor a perfect square on the left side: (m + -1)(m + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (m + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
m + -1 = 2.449489743 Simplifying m + -1 = 2.449489743 Reorder the terms: -1 + m = 2.449489743 Solving -1 + m = 2.449489743 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 = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + m = 2.449489743 + 1 m = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 m = 3.449489743 Simplifying m = 3.449489743Subproblem 2
m + -1 = -2.449489743 Simplifying m + -1 = -2.449489743 Reorder the terms: -1 + m = -2.449489743 Solving -1 + m = -2.449489743 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 = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + m = -2.449489743 + 1 m = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 m = -1.449489743 Simplifying m = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.449489743, -1.449489743}
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