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Simplifying 2m2 + 15m + 14 = 0 Reorder the terms: 14 + 15m + 2m2 = 0 Solving 14 + 15m + 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'. 7 + 7.5m + m2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 7.5m + -7 + m2 = 0 + -7 Reorder the terms: 7 + -7 + 7.5m + m2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 7.5m + m2 = 0 + -7 7.5m + m2 = 0 + -7 Combine like terms: 0 + -7 = -7 7.5m + m2 = -7 The m term is 7.5m. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5m + 14.0625 + m2 = -7 + 14.0625 Reorder the terms: 14.0625 + 7.5m + m2 = -7 + 14.0625 Combine like terms: -7 + 14.0625 = 7.0625 14.0625 + 7.5m + m2 = 7.0625 Factor a perfect square on the left side: (m + 3.75)(m + 3.75) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (m + 3.75) equal to 2.657536453 and -2.657536453.Subproblem 1
m + 3.75 = 2.657536453 Simplifying m + 3.75 = 2.657536453 Reorder the terms: 3.75 + m = 2.657536453 Solving 3.75 + m = 2.657536453 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + m = 2.657536453 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + m = 2.657536453 + -3.75 m = 2.657536453 + -3.75 Combine like terms: 2.657536453 + -3.75 = -1.092463547 m = -1.092463547 Simplifying m = -1.092463547Subproblem 2
m + 3.75 = -2.657536453 Simplifying m + 3.75 = -2.657536453 Reorder the terms: 3.75 + m = -2.657536453 Solving 3.75 + m = -2.657536453 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + m = -2.657536453 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + m = -2.657536453 + -3.75 m = -2.657536453 + -3.75 Combine like terms: -2.657536453 + -3.75 = -6.407536453 m = -6.407536453 Simplifying m = -6.407536453Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.092463547, -6.407536453}
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