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Simplifying 4m2 + 9m = 23 Reorder the terms: 9m + 4m2 = 23 Solving 9m + 4m2 = 23 Solving for variable 'm'. Reorder the terms: -23 + 9m + 4m2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 9m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + 2.25m + m2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + 2.25m + 5.75 + m2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + 2.25m + m2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + 2.25m + m2 = 0 + 5.75 2.25m + m2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 2.25m + m2 = 5.75 The m term is 2.25m. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25m + 1.265625 + m2 = 5.75 + 1.265625 Reorder the terms: 1.265625 + 2.25m + m2 = 5.75 + 1.265625 Combine like terms: 5.75 + 1.265625 = 7.015625 1.265625 + 2.25m + m2 = 7.015625 Factor a perfect square on the left side: (m + 1.125)(m + 1.125) = 7.015625 Calculate the square root of the right side: 2.648702513 Break this problem into two subproblems by setting (m + 1.125) equal to 2.648702513 and -2.648702513.Subproblem 1
m + 1.125 = 2.648702513 Simplifying m + 1.125 = 2.648702513 Reorder the terms: 1.125 + m = 2.648702513 Solving 1.125 + m = 2.648702513 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + m = 2.648702513 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + m = 2.648702513 + -1.125 m = 2.648702513 + -1.125 Combine like terms: 2.648702513 + -1.125 = 1.523702513 m = 1.523702513 Simplifying m = 1.523702513Subproblem 2
m + 1.125 = -2.648702513 Simplifying m + 1.125 = -2.648702513 Reorder the terms: 1.125 + m = -2.648702513 Solving 1.125 + m = -2.648702513 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + m = -2.648702513 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + m = -2.648702513 + -1.125 m = -2.648702513 + -1.125 Combine like terms: -2.648702513 + -1.125 = -3.773702513 m = -3.773702513 Simplifying m = -3.773702513Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.523702513, -3.773702513}
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