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Simplifying 4m2 = -3m + 15 Reorder the terms: 4m2 = 15 + -3m Solving 4m2 = 15 + -3m Solving for variable 'm'. Reorder the terms: -15 + 3m + 4m2 = 15 + -3m + -15 + 3m Reorder the terms: -15 + 3m + 4m2 = 15 + -15 + -3m + 3m Combine like terms: 15 + -15 = 0 -15 + 3m + 4m2 = 0 + -3m + 3m -15 + 3m + 4m2 = -3m + 3m Combine like terms: -3m + 3m = 0 -15 + 3m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + 0.75m + m2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + 0.75m + 3.75 + m2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + 0.75m + m2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + 0.75m + m2 = 0 + 3.75 0.75m + m2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 0.75m + m2 = 3.75 The m term is 0.75m. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75m + 0.140625 + m2 = 3.75 + 0.140625 Reorder the terms: 0.140625 + 0.75m + m2 = 3.75 + 0.140625 Combine like terms: 3.75 + 0.140625 = 3.890625 0.140625 + 0.75m + m2 = 3.890625 Factor a perfect square on the left side: (m + 0.375)(m + 0.375) = 3.890625 Calculate the square root of the right side: 1.97246673 Break this problem into two subproblems by setting (m + 0.375) equal to 1.97246673 and -1.97246673.Subproblem 1
m + 0.375 = 1.97246673 Simplifying m + 0.375 = 1.97246673 Reorder the terms: 0.375 + m = 1.97246673 Solving 0.375 + m = 1.97246673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + m = 1.97246673 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + m = 1.97246673 + -0.375 m = 1.97246673 + -0.375 Combine like terms: 1.97246673 + -0.375 = 1.59746673 m = 1.59746673 Simplifying m = 1.59746673Subproblem 2
m + 0.375 = -1.97246673 Simplifying m + 0.375 = -1.97246673 Reorder the terms: 0.375 + m = -1.97246673 Solving 0.375 + m = -1.97246673 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + m = -1.97246673 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + m = -1.97246673 + -0.375 m = -1.97246673 + -0.375 Combine like terms: -1.97246673 + -0.375 = -2.34746673 m = -2.34746673 Simplifying m = -2.34746673Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.59746673, -2.34746673}
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