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Simplifying 0.4m2 + 0.6m + -1.8 = 0 Reorder the terms: -1.8 + 0.6m + 0.4m2 = 0 Solving -1.8 + 0.6m + 0.4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -4.5 + 1.5m + m2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 1.5m + 4.5 + m2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 1.5m + m2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 1.5m + m2 = 0 + 4.5 1.5m + m2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 1.5m + m2 = 4.5 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 = 4.5 + 0.5625 Reorder the terms: 0.5625 + 1.5m + m2 = 4.5 + 0.5625 Combine like terms: 4.5 + 0.5625 = 5.0625 0.5625 + 1.5m + m2 = 5.0625 Factor a perfect square on the left side: (m + 0.75)(m + 0.75) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (m + 0.75) equal to 2.25 and -2.25.Subproblem 1
m + 0.75 = 2.25 Simplifying m + 0.75 = 2.25 Reorder the terms: 0.75 + m = 2.25 Solving 0.75 + m = 2.25 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 = 2.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m = 2.25 + -0.75 m = 2.25 + -0.75 Combine like terms: 2.25 + -0.75 = 1.5 m = 1.5 Simplifying m = 1.5Subproblem 2
m + 0.75 = -2.25 Simplifying m + 0.75 = -2.25 Reorder the terms: 0.75 + m = -2.25 Solving 0.75 + m = -2.25 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 = -2.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + m = -2.25 + -0.75 m = -2.25 + -0.75 Combine like terms: -2.25 + -0.75 = -3 m = -3 Simplifying m = -3Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.5, -3}
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