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Simplifying (m2 + 5m + -3) + -1(2m2 + -4m + 3) = 0 Reorder the terms: (-3 + 5m + m2) + -1(2m2 + -4m + 3) = 0 Remove parenthesis around (-3 + 5m + m2) -3 + 5m + m2 + -1(2m2 + -4m + 3) = 0 Reorder the terms: -3 + 5m + m2 + -1(3 + -4m + 2m2) = 0 -3 + 5m + m2 + (3 * -1 + -4m * -1 + 2m2 * -1) = 0 -3 + 5m + m2 + (-3 + 4m + -2m2) = 0 Reorder the terms: -3 + -3 + 5m + 4m + m2 + -2m2 = 0 Combine like terms: -3 + -3 = -6 -6 + 5m + 4m + m2 + -2m2 = 0 Combine like terms: 5m + 4m = 9m -6 + 9m + m2 + -2m2 = 0 Combine like terms: m2 + -2m2 = -1m2 -6 + 9m + -1m2 = 0 Solving -6 + 9m + -1m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 6 + -9m + m2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -9m + -6 + m2 = 0 + -6 Reorder the terms: 6 + -6 + -9m + m2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -9m + m2 = 0 + -6 -9m + m2 = 0 + -6 Combine like terms: 0 + -6 = -6 -9m + m2 = -6 The m term is -9m. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9m + 20.25 + m2 = -6 + 20.25 Reorder the terms: 20.25 + -9m + m2 = -6 + 20.25 Combine like terms: -6 + 20.25 = 14.25 20.25 + -9m + m2 = 14.25 Factor a perfect square on the left side: (m + -4.5)(m + -4.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (m + -4.5) equal to 3.774917218 and -3.774917218.Subproblem 1
m + -4.5 = 3.774917218 Simplifying m + -4.5 = 3.774917218 Reorder the terms: -4.5 + m = 3.774917218 Solving -4.5 + m = 3.774917218 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = 3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = 3.774917218 + 4.5 m = 3.774917218 + 4.5 Combine like terms: 3.774917218 + 4.5 = 8.274917218 m = 8.274917218 Simplifying m = 8.274917218Subproblem 2
m + -4.5 = -3.774917218 Simplifying m + -4.5 = -3.774917218 Reorder the terms: -4.5 + m = -3.774917218 Solving -4.5 + m = -3.774917218 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + m = -3.774917218 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + m = -3.774917218 + 4.5 m = -3.774917218 + 4.5 Combine like terms: -3.774917218 + 4.5 = 0.725082782 m = 0.725082782 Simplifying m = 0.725082782Solution
The solution to the problem is based on the solutions from the subproblems. m = {8.274917218, 0.725082782}
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