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Simplifying (7m2 + 3m + -4) + -1(3m2 + 9m + -5) = 0 Reorder the terms: (-4 + 3m + 7m2) + -1(3m2 + 9m + -5) = 0 Remove parenthesis around (-4 + 3m + 7m2) -4 + 3m + 7m2 + -1(3m2 + 9m + -5) = 0 Reorder the terms: -4 + 3m + 7m2 + -1(-5 + 9m + 3m2) = 0 -4 + 3m + 7m2 + (-5 * -1 + 9m * -1 + 3m2 * -1) = 0 -4 + 3m + 7m2 + (5 + -9m + -3m2) = 0 Reorder the terms: -4 + 5 + 3m + -9m + 7m2 + -3m2 = 0 Combine like terms: -4 + 5 = 1 1 + 3m + -9m + 7m2 + -3m2 = 0 Combine like terms: 3m + -9m = -6m 1 + -6m + 7m2 + -3m2 = 0 Combine like terms: 7m2 + -3m2 = 4m2 1 + -6m + 4m2 = 0 Solving 1 + -6m + 4m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -1.5m + m2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.5m + -0.25 + m2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.5m + m2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.5m + m2 = 0 + -0.25 -1.5m + m2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.5m + m2 = -0.25 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 = -0.25 + 0.5625 Reorder the terms: 0.5625 + -1.5m + m2 = -0.25 + 0.5625 Combine like terms: -0.25 + 0.5625 = 0.3125 0.5625 + -1.5m + m2 = 0.3125 Factor a perfect square on the left side: (m + -0.75)(m + -0.75) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (m + -0.75) equal to 0.559016994 and -0.559016994.Subproblem 1
m + -0.75 = 0.559016994 Simplifying m + -0.75 = 0.559016994 Reorder the terms: -0.75 + m = 0.559016994 Solving -0.75 + m = 0.559016994 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 = 0.559016994 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = 0.559016994 + 0.75 m = 0.559016994 + 0.75 Combine like terms: 0.559016994 + 0.75 = 1.309016994 m = 1.309016994 Simplifying m = 1.309016994Subproblem 2
m + -0.75 = -0.559016994 Simplifying m + -0.75 = -0.559016994 Reorder the terms: -0.75 + m = -0.559016994 Solving -0.75 + m = -0.559016994 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 = -0.559016994 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + m = -0.559016994 + 0.75 m = -0.559016994 + 0.75 Combine like terms: -0.559016994 + 0.75 = 0.190983006 m = 0.190983006 Simplifying m = 0.190983006Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.309016994, 0.190983006}
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