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Simplifying 4m(m + -1) = 2m + 3 Reorder the terms: 4m(-1 + m) = 2m + 3 (-1 * 4m + m * 4m) = 2m + 3 (-4m + 4m2) = 2m + 3 Reorder the terms: -4m + 4m2 = 3 + 2m Solving -4m + 4m2 = 3 + 2m Solving for variable 'm'. Reorder the terms: -3 + -4m + -2m + 4m2 = 3 + 2m + -3 + -2m Combine like terms: -4m + -2m = -6m -3 + -6m + 4m2 = 3 + 2m + -3 + -2m Reorder the terms: -3 + -6m + 4m2 = 3 + -3 + 2m + -2m Combine like terms: 3 + -3 = 0 -3 + -6m + 4m2 = 0 + 2m + -2m -3 + -6m + 4m2 = 2m + -2m Combine like terms: 2m + -2m = 0 -3 + -6m + 4m2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -1.5m + m2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.5m + 0.75 + m2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.5m + m2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.5m + m2 = 0 + 0.75 -1.5m + m2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.5m + m2 = 0.75 The m term is -1.5m. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5m + 0.5625 + m2 = 0.75 + 0.5625 Reorder the terms: 0.5625 + -1.5m + m2 = 0.75 + 0.5625 Combine like terms: 0.75 + 0.5625 = 1.3125 0.5625 + -1.5m + m2 = 1.3125 Factor a perfect square on the left side: (m + -0.75)(m + -0.75) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (m + -0.75) equal to 1.145643924 and -1.145643924.Subproblem 1
m + -0.75 = 1.145643924 Simplifying m + -0.75 = 1.145643924 Reorder the terms: -0.75 + m = 1.145643924 Solving -0.75 + m = 1.145643924 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = 1.145643924 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = 1.145643924 + 0.75 m = 1.145643924 + 0.75 Combine like terms: 1.145643924 + 0.75 = 1.895643924 m = 1.895643924 Simplifying m = 1.895643924Subproblem 2
m + -0.75 = -1.145643924 Simplifying m + -0.75 = -1.145643924 Reorder the terms: -0.75 + m = -1.145643924 Solving -0.75 + m = -1.145643924 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + m = -1.145643924 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = -1.145643924 + 0.75 m = -1.145643924 + 0.75 Combine like terms: -1.145643924 + 0.75 = -0.395643924 m = -0.395643924 Simplifying m = -0.395643924Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.895643924, -0.395643924}
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