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Simplifying 2m2 + 5m + -13 = 0 Reorder the terms: -13 + 5m + 2m2 = 0 Solving -13 + 5m + 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 + 2.5m + m2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + 2.5m + 6.5 + m2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + 2.5m + m2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + 2.5m + m2 = 0 + 6.5 2.5m + m2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 2.5m + m2 = 6.5 The m term is 2.5m. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5m + 1.5625 + m2 = 6.5 + 1.5625 Reorder the terms: 1.5625 + 2.5m + m2 = 6.5 + 1.5625 Combine like terms: 6.5 + 1.5625 = 8.0625 1.5625 + 2.5m + m2 = 8.0625 Factor a perfect square on the left side: (m + 1.25)(m + 1.25) = 8.0625 Calculate the square root of the right side: 2.839454173 Break this problem into two subproblems by setting (m + 1.25) equal to 2.839454173 and -2.839454173.Subproblem 1
m + 1.25 = 2.839454173 Simplifying m + 1.25 = 2.839454173 Reorder the terms: 1.25 + m = 2.839454173 Solving 1.25 + m = 2.839454173 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + m = 2.839454173 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = 2.839454173 + -1.25 m = 2.839454173 + -1.25 Combine like terms: 2.839454173 + -1.25 = 1.589454173 m = 1.589454173 Simplifying m = 1.589454173Subproblem 2
m + 1.25 = -2.839454173 Simplifying m + 1.25 = -2.839454173 Reorder the terms: 1.25 + m = -2.839454173 Solving 1.25 + m = -2.839454173 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + m = -2.839454173 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = -2.839454173 + -1.25 m = -2.839454173 + -1.25 Combine like terms: -2.839454173 + -1.25 = -4.089454173 m = -4.089454173 Simplifying m = -4.089454173Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.589454173, -4.089454173}
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