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Simplifying 2m2 + 13m + 14 = 0 Reorder the terms: 14 + 13m + 2m2 = 0 Solving 14 + 13m + 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 + 6.5m + m2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 6.5m + -7 + m2 = 0 + -7 Reorder the terms: 7 + -7 + 6.5m + m2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6.5m + m2 = 0 + -7 6.5m + m2 = 0 + -7 Combine like terms: 0 + -7 = -7 6.5m + m2 = -7 The m term is 6.5m. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5m + 10.5625 + m2 = -7 + 10.5625 Reorder the terms: 10.5625 + 6.5m + m2 = -7 + 10.5625 Combine like terms: -7 + 10.5625 = 3.5625 10.5625 + 6.5m + m2 = 3.5625 Factor a perfect square on the left side: (m + 3.25)(m + 3.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (m + 3.25) equal to 1.887458609 and -1.887458609.Subproblem 1
m + 3.25 = 1.887458609 Simplifying m + 3.25 = 1.887458609 Reorder the terms: 3.25 + m = 1.887458609 Solving 3.25 + m = 1.887458609 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + m = 1.887458609 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + m = 1.887458609 + -3.25 m = 1.887458609 + -3.25 Combine like terms: 1.887458609 + -3.25 = -1.362541391 m = -1.362541391 Simplifying m = -1.362541391Subproblem 2
m + 3.25 = -1.887458609 Simplifying m + 3.25 = -1.887458609 Reorder the terms: 3.25 + m = -1.887458609 Solving 3.25 + m = -1.887458609 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + m = -1.887458609 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + m = -1.887458609 + -3.25 m = -1.887458609 + -3.25 Combine like terms: -1.887458609 + -3.25 = -5.137458609 m = -5.137458609 Simplifying m = -5.137458609Solution
The solution to the problem is based on the solutions from the subproblems. m = {-1.362541391, -5.137458609}
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