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Simplifying 3m2 + 17m + 6 = 0 Reorder the terms: 6 + 17m + 3m2 = 0 Solving 6 + 17m + 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'. 2 + 5.666666667m + m2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 5.666666667m + -2 + m2 = 0 + -2 Reorder the terms: 2 + -2 + 5.666666667m + m2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5.666666667m + m2 = 0 + -2 5.666666667m + m2 = 0 + -2 Combine like terms: 0 + -2 = -2 5.666666667m + m2 = -2 The m term is 5.666666667m. Take half its coefficient (2.833333334). Square it (8.027777782) and add it to both sides. Add '8.027777782' to each side of the equation. 5.666666667m + 8.027777782 + m2 = -2 + 8.027777782 Reorder the terms: 8.027777782 + 5.666666667m + m2 = -2 + 8.027777782 Combine like terms: -2 + 8.027777782 = 6.027777782 8.027777782 + 5.666666667m + m2 = 6.027777782 Factor a perfect square on the left side: (m + 2.833333334)(m + 2.833333334) = 6.027777782 Calculate the square root of the right side: 2.455153311 Break this problem into two subproblems by setting (m + 2.833333334) equal to 2.455153311 and -2.455153311.Subproblem 1
m + 2.833333334 = 2.455153311 Simplifying m + 2.833333334 = 2.455153311 Reorder the terms: 2.833333334 + m = 2.455153311 Solving 2.833333334 + m = 2.455153311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + m = 2.455153311 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + m = 2.455153311 + -2.833333334 m = 2.455153311 + -2.833333334 Combine like terms: 2.455153311 + -2.833333334 = -0.378180023 m = -0.378180023 Simplifying m = -0.378180023Subproblem 2
m + 2.833333334 = -2.455153311 Simplifying m + 2.833333334 = -2.455153311 Reorder the terms: 2.833333334 + m = -2.455153311 Solving 2.833333334 + m = -2.455153311 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-2.833333334' to each side of the equation. 2.833333334 + -2.833333334 + m = -2.455153311 + -2.833333334 Combine like terms: 2.833333334 + -2.833333334 = 0.000000000 0.000000000 + m = -2.455153311 + -2.833333334 m = -2.455153311 + -2.833333334 Combine like terms: -2.455153311 + -2.833333334 = -5.288486645 m = -5.288486645 Simplifying m = -5.288486645Solution
The solution to the problem is based on the solutions from the subproblems. m = {-0.378180023, -5.288486645}
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