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Simplifying 3m + -2m(m + -3) = 1 Reorder the terms: 3m + -2m(-3 + m) = 1 3m + (-3 * -2m + m * -2m) = 1 3m + (6m + -2m2) = 1 Combine like terms: 3m + 6m = 9m 9m + -2m2 = 1 Solving 9m + -2m2 = 1 Solving for variable 'm'. Reorder the terms: -1 + 9m + -2m2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 9m + -2m2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.5 + -4.5m + m2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -4.5m + -0.5 + m2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -4.5m + m2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -4.5m + m2 = 0 + -0.5 -4.5m + m2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -4.5m + m2 = -0.5 The m term is -4.5m. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5m + 5.0625 + m2 = -0.5 + 5.0625 Reorder the terms: 5.0625 + -4.5m + m2 = -0.5 + 5.0625 Combine like terms: -0.5 + 5.0625 = 4.5625 5.0625 + -4.5m + m2 = 4.5625 Factor a perfect square on the left side: (m + -2.25)(m + -2.25) = 4.5625 Calculate the square root of the right side: 2.136000936 Break this problem into two subproblems by setting (m + -2.25) equal to 2.136000936 and -2.136000936.Subproblem 1
m + -2.25 = 2.136000936 Simplifying m + -2.25 = 2.136000936 Reorder the terms: -2.25 + m = 2.136000936 Solving -2.25 + m = 2.136000936 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + m = 2.136000936 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + m = 2.136000936 + 2.25 m = 2.136000936 + 2.25 Combine like terms: 2.136000936 + 2.25 = 4.386000936 m = 4.386000936 Simplifying m = 4.386000936Subproblem 2
m + -2.25 = -2.136000936 Simplifying m + -2.25 = -2.136000936 Reorder the terms: -2.25 + m = -2.136000936 Solving -2.25 + m = -2.136000936 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + m = -2.136000936 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + m = -2.136000936 + 2.25 m = -2.136000936 + 2.25 Combine like terms: -2.136000936 + 2.25 = 0.113999064 m = 0.113999064 Simplifying m = 0.113999064Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.386000936, 0.113999064}
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