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Simplifying 2m(m + -2) + -1(3m + 1)(m + -3) = 0 Reorder the terms: 2m(-2 + m) + -1(3m + 1)(m + -3) = 0 (-2 * 2m + m * 2m) + -1(3m + 1)(m + -3) = 0 (-4m + 2m2) + -1(3m + 1)(m + -3) = 0 Reorder the terms: -4m + 2m2 + -1(1 + 3m)(m + -3) = 0 Reorder the terms: -4m + 2m2 + -1(1 + 3m)(-3 + m) = 0 Multiply (1 + 3m) * (-3 + m) -4m + 2m2 + -1(1(-3 + m) + 3m * (-3 + m)) = 0 -4m + 2m2 + -1((-3 * 1 + m * 1) + 3m * (-3 + m)) = 0 -4m + 2m2 + -1((-3 + 1m) + 3m * (-3 + m)) = 0 -4m + 2m2 + -1(-3 + 1m + (-3 * 3m + m * 3m)) = 0 -4m + 2m2 + -1(-3 + 1m + (-9m + 3m2)) = 0 Combine like terms: 1m + -9m = -8m -4m + 2m2 + -1(-3 + -8m + 3m2) = 0 -4m + 2m2 + (-3 * -1 + -8m * -1 + 3m2 * -1) = 0 -4m + 2m2 + (3 + 8m + -3m2) = 0 Reorder the terms: 3 + -4m + 8m + 2m2 + -3m2 = 0 Combine like terms: -4m + 8m = 4m 3 + 4m + 2m2 + -3m2 = 0 Combine like terms: 2m2 + -3m2 = -1m2 3 + 4m + -1m2 = 0 Solving 3 + 4m + -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'. -3 + -4m + m2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -4m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + -4m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4m + m2 = 0 + 3 -4m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4m + m2 = 3 The m term is -4m. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4m + 4 + m2 = 3 + 4 Reorder the terms: 4 + -4m + m2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + -4m + m2 = 7 Factor a perfect square on the left side: (m + -2)(m + -2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (m + -2) equal to 2.645751311 and -2.645751311.Subproblem 1
m + -2 = 2.645751311 Simplifying m + -2 = 2.645751311 Reorder the terms: -2 + m = 2.645751311 Solving -2 + m = 2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + m = 2.645751311 + 2 m = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 m = 4.645751311 Simplifying m = 4.645751311Subproblem 2
m + -2 = -2.645751311 Simplifying m + -2 = -2.645751311 Reorder the terms: -2 + m = -2.645751311 Solving -2 + m = -2.645751311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + m = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + m = -2.645751311 + 2 m = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 m = -0.645751311 Simplifying m = -0.645751311Solution
The solution to the problem is based on the solutions from the subproblems. m = {4.645751311, -0.645751311}
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