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Simplifying 2m2 + 5m + -130 = 0 Reorder the terms: -130 + 5m + 2m2 = 0 Solving -130 + 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'. -65 + 2.5m + m2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + 2.5m + 65 + m2 = 0 + 65 Reorder the terms: -65 + 65 + 2.5m + m2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + 2.5m + m2 = 0 + 65 2.5m + m2 = 0 + 65 Combine like terms: 0 + 65 = 65 2.5m + m2 = 65 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 = 65 + 1.5625 Reorder the terms: 1.5625 + 2.5m + m2 = 65 + 1.5625 Combine like terms: 65 + 1.5625 = 66.5625 1.5625 + 2.5m + m2 = 66.5625 Factor a perfect square on the left side: (m + 1.25)(m + 1.25) = 66.5625 Calculate the square root of the right side: 8.158584436 Break this problem into two subproblems by setting (m + 1.25) equal to 8.158584436 and -8.158584436.Subproblem 1
m + 1.25 = 8.158584436 Simplifying m + 1.25 = 8.158584436 Reorder the terms: 1.25 + m = 8.158584436 Solving 1.25 + m = 8.158584436 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 = 8.158584436 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = 8.158584436 + -1.25 m = 8.158584436 + -1.25 Combine like terms: 8.158584436 + -1.25 = 6.908584436 m = 6.908584436 Simplifying m = 6.908584436Subproblem 2
m + 1.25 = -8.158584436 Simplifying m + 1.25 = -8.158584436 Reorder the terms: 1.25 + m = -8.158584436 Solving 1.25 + m = -8.158584436 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 = -8.158584436 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + m = -8.158584436 + -1.25 m = -8.158584436 + -1.25 Combine like terms: -8.158584436 + -1.25 = -9.408584436 m = -9.408584436 Simplifying m = -9.408584436Solution
The solution to the problem is based on the solutions from the subproblems. m = {6.908584436, -9.408584436}
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