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Simplifying m2 = 6m + 19 Reorder the terms: m2 = 19 + 6m Solving m2 = 19 + 6m Solving for variable 'm'. Reorder the terms: -19 + -6m + m2 = 19 + 6m + -19 + -6m Reorder the terms: -19 + -6m + m2 = 19 + -19 + 6m + -6m Combine like terms: 19 + -19 = 0 -19 + -6m + m2 = 0 + 6m + -6m -19 + -6m + m2 = 6m + -6m Combine like terms: 6m + -6m = 0 -19 + -6m + m2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -6m + 19 + m2 = 0 + 19 Reorder the terms: -19 + 19 + -6m + m2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -6m + m2 = 0 + 19 -6m + m2 = 0 + 19 Combine like terms: 0 + 19 = 19 -6m + m2 = 19 The m term is -6m. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6m + 9 + m2 = 19 + 9 Reorder the terms: 9 + -6m + m2 = 19 + 9 Combine like terms: 19 + 9 = 28 9 + -6m + m2 = 28 Factor a perfect square on the left side: (m + -3)(m + -3) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (m + -3) equal to 5.291502622 and -5.291502622.Subproblem 1
m + -3 = 5.291502622 Simplifying m + -3 = 5.291502622 Reorder the terms: -3 + m = 5.291502622 Solving -3 + m = 5.291502622 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = 5.291502622 + 3 Combine like terms: -3 + 3 = 0 0 + m = 5.291502622 + 3 m = 5.291502622 + 3 Combine like terms: 5.291502622 + 3 = 8.291502622 m = 8.291502622 Simplifying m = 8.291502622Subproblem 2
m + -3 = -5.291502622 Simplifying m + -3 = -5.291502622 Reorder the terms: -3 + m = -5.291502622 Solving -3 + m = -5.291502622 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + m = -5.291502622 + 3 Combine like terms: -3 + 3 = 0 0 + m = -5.291502622 + 3 m = -5.291502622 + 3 Combine like terms: -5.291502622 + 3 = -2.291502622 m = -2.291502622 Simplifying m = -2.291502622Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.291502622, -2.291502622}
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