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Simplifying (3m + 4) + -1(2m2 + -6m + 5) = 0 Reorder the terms: (4 + 3m) + -1(2m2 + -6m + 5) = 0 Remove parenthesis around (4 + 3m) 4 + 3m + -1(2m2 + -6m + 5) = 0 Reorder the terms: 4 + 3m + -1(5 + -6m + 2m2) = 0 4 + 3m + (5 * -1 + -6m * -1 + 2m2 * -1) = 0 4 + 3m + (-5 + 6m + -2m2) = 0 Reorder the terms: 4 + -5 + 3m + 6m + -2m2 = 0 Combine like terms: 4 + -5 = -1 -1 + 3m + 6m + -2m2 = 0 Combine like terms: 3m + 6m = 9m -1 + 9m + -2m2 = 0 Solving -1 + 9m + -2m2 = 0 Solving for variable 'm'. 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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