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Simplifying 2m2 + 13m + -16 = 0 Reorder the terms: -16 + 13m + 2m2 = 0 Solving -16 + 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'. -8 + 6.5m + m2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 6.5m + 8 + m2 = 0 + 8 Reorder the terms: -8 + 8 + 6.5m + m2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 6.5m + m2 = 0 + 8 6.5m + m2 = 0 + 8 Combine like terms: 0 + 8 = 8 6.5m + m2 = 8 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 = 8 + 10.5625 Reorder the terms: 10.5625 + 6.5m + m2 = 8 + 10.5625 Combine like terms: 8 + 10.5625 = 18.5625 10.5625 + 6.5m + m2 = 18.5625 Factor a perfect square on the left side: (m + 3.25)(m + 3.25) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (m + 3.25) equal to 4.308421985 and -4.308421985.Subproblem 1
m + 3.25 = 4.308421985 Simplifying m + 3.25 = 4.308421985 Reorder the terms: 3.25 + m = 4.308421985 Solving 3.25 + m = 4.308421985 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 = 4.308421985 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + m = 4.308421985 + -3.25 m = 4.308421985 + -3.25 Combine like terms: 4.308421985 + -3.25 = 1.058421985 m = 1.058421985 Simplifying m = 1.058421985Subproblem 2
m + 3.25 = -4.308421985 Simplifying m + 3.25 = -4.308421985 Reorder the terms: 3.25 + m = -4.308421985 Solving 3.25 + m = -4.308421985 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 = -4.308421985 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + m = -4.308421985 + -3.25 m = -4.308421985 + -3.25 Combine like terms: -4.308421985 + -3.25 = -7.558421985 m = -7.558421985 Simplifying m = -7.558421985Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.058421985, -7.558421985}
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