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Simplifying 3m2 + m + -9 = 0 Reorder the terms: -9 + m + 3m2 = 0 Solving -9 + m + 3m2 = 0 Solving for variable 'm'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 0.3333333333m + m2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.3333333333m + 3 + m2 = 0 + 3 Reorder the terms: -3 + 3 + 0.3333333333m + m2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.3333333333m + m2 = 0 + 3 0.3333333333m + m2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.3333333333m + m2 = 3 The m term is m. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333m + 0.25 + m2 = 3 + 0.25 Reorder the terms: 0.25 + 0.3333333333m + m2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + 0.3333333333m + m2 = 3.25 Factor a perfect square on the left side: (m + 0.5)(m + 0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (m + 0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
m + 0.5 = 1.802775638 Simplifying m + 0.5 = 1.802775638 Reorder the terms: 0.5 + m = 1.802775638 Solving 0.5 + m = 1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = 1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = 1.802775638 + -0.5 m = 1.802775638 + -0.5 Combine like terms: 1.802775638 + -0.5 = 1.302775638 m = 1.302775638 Simplifying m = 1.302775638Subproblem 2
m + 0.5 = -1.802775638 Simplifying m + 0.5 = -1.802775638 Reorder the terms: 0.5 + m = -1.802775638 Solving 0.5 + m = -1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + m = -1.802775638 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + m = -1.802775638 + -0.5 m = -1.802775638 + -0.5 Combine like terms: -1.802775638 + -0.5 = -2.302775638 m = -2.302775638 Simplifying m = -2.302775638Solution
The solution to the problem is based on the solutions from the subproblems. m = {1.302775638, -2.302775638}
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