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Simplifying 2m2 + 5m + -28 = 0 Reorder the terms: -28 + 5m + 2m2 = 0 Solving -28 + 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'. -14 + 2.5m + m2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 2.5m + 14 + m2 = 0 + 14 Reorder the terms: -14 + 14 + 2.5m + m2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 2.5m + m2 = 0 + 14 2.5m + m2 = 0 + 14 Combine like terms: 0 + 14 = 14 2.5m + m2 = 14 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 = 14 + 1.5625 Reorder the terms: 1.5625 + 2.5m + m2 = 14 + 1.5625 Combine like terms: 14 + 1.5625 = 15.5625 1.5625 + 2.5m + m2 = 15.5625 Factor a perfect square on the left side: (m + 1.25)(m + 1.25) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (m + 1.25) equal to 3.94493346 and -3.94493346.Subproblem 1
m + 1.25 = 3.94493346 Simplifying m + 1.25 = 3.94493346 Reorder the terms: 1.25 + m = 3.94493346 Solving 1.25 + m = 3.94493346 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 = 3.94493346 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = 3.94493346 + -1.25 m = 3.94493346 + -1.25 Combine like terms: 3.94493346 + -1.25 = 2.69493346 m = 2.69493346 Simplifying m = 2.69493346Subproblem 2
m + 1.25 = -3.94493346 Simplifying m + 1.25 = -3.94493346 Reorder the terms: 1.25 + m = -3.94493346 Solving 1.25 + m = -3.94493346 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 = -3.94493346 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = -3.94493346 + -1.25 m = -3.94493346 + -1.25 Combine like terms: -3.94493346 + -1.25 = -5.19493346 m = -5.19493346 Simplifying m = -5.19493346Solution
The solution to the problem is based on the solutions from the subproblems. m = {2.69493346, -5.19493346}
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