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Simplifying 2m2 + 17m + 22 = 0 Reorder the terms: 22 + 17m + 2m2 = 0 Solving 22 + 17m + 2m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11 + 8.5m + m2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + 8.5m + -11 + m2 = 0 + -11 Reorder the terms: 11 + -11 + 8.5m + m2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 8.5m + m2 = 0 + -11 8.5m + m2 = 0 + -11 Combine like terms: 0 + -11 = -11 8.5m + m2 = -11 The m term is 8.5m. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5m + 18.0625 + m2 = -11 + 18.0625 Reorder the terms: 18.0625 + 8.5m + m2 = -11 + 18.0625 Combine like terms: -11 + 18.0625 = 7.0625 18.0625 + 8.5m + m2 = 7.0625 Factor a perfect square on the left side: (m + 4.25)(m + 4.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (m + 4.25) equal to 2.657536453 and -2.657536453.Subproblem 1
m + 4.25 = 2.657536453 Simplifying m + 4.25 = 2.657536453 Reorder the terms: 4.25 + m = 2.657536453 Solving 4.25 + m = 2.657536453 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + m = 2.657536453 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + m = 2.657536453 + -4.25 m = 2.657536453 + -4.25 Combine like terms: 2.657536453 + -4.25 = -1.592463547 m = -1.592463547 Simplifying m = -1.592463547Subproblem 2
m + 4.25 = -2.657536453 Simplifying m + 4.25 = -2.657536453 Reorder the terms: 4.25 + m = -2.657536453 Solving 4.25 + m = -2.657536453 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + m = -2.657536453 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + m = -2.657536453 + -4.25 m = -2.657536453 + -4.25 Combine like terms: -2.657536453 + -4.25 = -6.907536453 m = -6.907536453 Simplifying m = -6.907536453Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.592463547, -6.907536453}
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