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Simplifying m2 + 3m + -1 = 0 Reorder the terms: -1 + 3m + m2 = 0 Solving -1 + 3m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 3m + 1 + m2 = 0 + 1 Reorder the terms: -1 + 1 + 3m + m2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3m + m2 = 0 + 1 3m + m2 = 0 + 1 Combine like terms: 0 + 1 = 1 3m + m2 = 1 The m term is 3m. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3m + 2.25 + m2 = 1 + 2.25 Reorder the terms: 2.25 + 3m + m2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + 3m + m2 = 3.25 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (m + 1.5) equal to 1.802775638 and -1.802775638.Subproblem 1
m + 1.5 = 1.802775638 Simplifying m + 1.5 = 1.802775638 Reorder the terms: 1.5 + m = 1.802775638 Solving 1.5 + m = 1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = 1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 1.802775638 + -1.5 m = 1.802775638 + -1.5 Combine like terms: 1.802775638 + -1.5 = 0.302775638 m = 0.302775638 Simplifying m = 0.302775638Subproblem 2
m + 1.5 = -1.802775638 Simplifying m + 1.5 = -1.802775638 Reorder the terms: 1.5 + m = -1.802775638 Solving 1.5 + m = -1.802775638 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + m = -1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -1.802775638 + -1.5 m = -1.802775638 + -1.5 Combine like terms: -1.802775638 + -1.5 = -3.302775638 m = -3.302775638 Simplifying m = -3.302775638Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.302775638, -3.302775638}
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