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Simplifying -1m2 + -6m + 3 = 0 Reorder the terms: 3 + -6m + -1m2 = 0 Solving 3 + -6m + -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 + 6m + m2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 6m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + 6m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 6m + m2 = 0 + 3 6m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 6m + m2 = 3 The m term is 6m. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6m + 9 + m2 = 3 + 9 Reorder the terms: 9 + 6m + m2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + 6m + m2 = 12 Factor a perfect square on the left side: (m + 3)(m + 3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (m + 3) equal to 3.464101615 and -3.464101615.Subproblem 1
m + 3 = 3.464101615 Simplifying m + 3 = 3.464101615 Reorder the terms: 3 + m = 3.464101615 Solving 3 + m = 3.464101615 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + m = 3.464101615 + -3 m = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 m = 0.464101615 Simplifying m = 0.464101615Subproblem 2
m + 3 = -3.464101615 Simplifying m + 3 = -3.464101615 Reorder the terms: 3 + m = -3.464101615 Solving 3 + m = -3.464101615 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + m = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + m = -3.464101615 + -3 m = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 m = -6.464101615 Simplifying m = -6.464101615Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.464101615, -6.464101615}
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