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Simplifying m2 + 3m + -2 = 0 Reorder the terms: -2 + 3m + m2 = 0 Solving -2 + 3m + m2 = 0 Solving for variable 'm'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 3m + 2 + m2 = 0 + 2 Reorder the terms: -2 + 2 + 3m + m2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3m + m2 = 0 + 2 3m + m2 = 0 + 2 Combine like terms: 0 + 2 = 2 3m + m2 = 2 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 = 2 + 2.25 Reorder the terms: 2.25 + 3m + m2 = 2 + 2.25 Combine like terms: 2 + 2.25 = 4.25 2.25 + 3m + m2 = 4.25 Factor a perfect square on the left side: (m + 1.5)(m + 1.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (m + 1.5) equal to 2.061552813 and -2.061552813.Subproblem 1
m + 1.5 = 2.061552813 Simplifying m + 1.5 = 2.061552813 Reorder the terms: 1.5 + m = 2.061552813 Solving 1.5 + m = 2.061552813 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 = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = 2.061552813 + -1.5 m = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 m = 0.561552813 Simplifying m = 0.561552813Subproblem 2
m + 1.5 = -2.061552813 Simplifying m + 1.5 = -2.061552813 Reorder the terms: 1.5 + m = -2.061552813 Solving 1.5 + m = -2.061552813 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 = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + m = -2.061552813 + -1.5 m = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 m = -3.561552813 Simplifying m = -3.561552813Solution
The solution to the problem is based on the solutions from the subproblems. m = {0.561552813, -3.561552813}
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