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Simplifying 0.5m(2m + -3) + -0.8m = 2.7 Reorder the terms: 0.5m(-3 + 2m) + -0.8m = 2.7 (-3 * 0.5m + 2m * 0.5m) + -0.8m = 2.7 (-1.5m + 1m2) + -0.8m = 2.7 Reorder the terms: -1.5m + -0.8m + 1m2 = 2.7 Combine like terms: -1.5m + -0.8m = -2.3m -2.3m + 1m2 = 2.7 Solving -2.3m + 1m2 = 2.7 Solving for variable 'm'. Reorder the terms: -2.7 + -2.3m + 1m2 = 2.7 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 -2.7 + -2.3m + 1m2 = 0.0 Begin completing the square. Move the constant term to the right: Add '2.7' to each side of the equation. -2.7 + -2.3m + 2.7 + m2 = 0.0 + 2.7 Reorder the terms: -2.7 + 2.7 + -2.3m + m2 = 0.0 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + -2.3m + m2 = 0.0 + 2.7 -2.3m + m2 = 0.0 + 2.7 Combine like terms: 0.0 + 2.7 = 2.7 -2.3m + m2 = 2.7 The m term is -2.3m. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3m + 1.3225 + m2 = 2.7 + 1.3225 Reorder the terms: 1.3225 + -2.3m + m2 = 2.7 + 1.3225 Combine like terms: 2.7 + 1.3225 = 4.0225 1.3225 + -2.3m + m2 = 4.0225 Factor a perfect square on the left side: (m + -1.15)(m + -1.15) = 4.0225 Calculate the square root of the right side: 2.005617112 Break this problem into two subproblems by setting (m + -1.15) equal to 2.005617112 and -2.005617112.Subproblem 1
m + -1.15 = 2.005617112 Simplifying m + -1.15 = 2.005617112 Reorder the terms: -1.15 + m = 2.005617112 Solving -1.15 + m = 2.005617112 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + m = 2.005617112 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + m = 2.005617112 + 1.15 m = 2.005617112 + 1.15 Combine like terms: 2.005617112 + 1.15 = 3.155617112 m = 3.155617112 Simplifying m = 3.155617112Subproblem 2
m + -1.15 = -2.005617112 Simplifying m + -1.15 = -2.005617112 Reorder the terms: -1.15 + m = -2.005617112 Solving -1.15 + m = -2.005617112 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + m = -2.005617112 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + m = -2.005617112 + 1.15 m = -2.005617112 + 1.15 Combine like terms: -2.005617112 + 1.15 = -0.855617112 m = -0.855617112 Simplifying m = -0.855617112Solution
The solution to the problem is based on the solutions from the subproblems. m = {3.155617112, -0.855617112}
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