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Simplifying 13 + 2m2 + 14m = 0 Reorder the terms: 13 + 14m + 2m2 = 0 Solving 13 + 14m + 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'. 6.5 + 7m + m2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + 7m + -6.5 + m2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + 7m + m2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + 7m + m2 = 0 + -6.5 7m + m2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 7m + m2 = -6.5 The m term is 7m. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7m + 12.25 + m2 = -6.5 + 12.25 Reorder the terms: 12.25 + 7m + m2 = -6.5 + 12.25 Combine like terms: -6.5 + 12.25 = 5.75 12.25 + 7m + m2 = 5.75 Factor a perfect square on the left side: (m + 3.5)(m + 3.5) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (m + 3.5) equal to 2.397915762 and -2.397915762.Subproblem 1
m + 3.5 = 2.397915762 Simplifying m + 3.5 = 2.397915762 Reorder the terms: 3.5 + m = 2.397915762 Solving 3.5 + m = 2.397915762 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = 2.397915762 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = 2.397915762 + -3.5 m = 2.397915762 + -3.5 Combine like terms: 2.397915762 + -3.5 = -1.102084238 m = -1.102084238 Simplifying m = -1.102084238Subproblem 2
m + 3.5 = -2.397915762 Simplifying m + 3.5 = -2.397915762 Reorder the terms: 3.5 + m = -2.397915762 Solving 3.5 + m = -2.397915762 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + m = -2.397915762 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + m = -2.397915762 + -3.5 m = -2.397915762 + -3.5 Combine like terms: -2.397915762 + -3.5 = -5.897915762 m = -5.897915762 Simplifying m = -5.897915762Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.102084238, -5.897915762}
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