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Simplifying 3x2 + 82x + 418 = 0 Reorder the terms: 418 + 82x + 3x2 = 0 Solving 418 + 82x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 139.3333333 + 27.33333333x + x2 = 0 Move the constant term to the right: Add '-139.3333333' to each side of the equation. 139.3333333 + 27.33333333x + -139.3333333 + x2 = 0 + -139.3333333 Reorder the terms: 139.3333333 + -139.3333333 + 27.33333333x + x2 = 0 + -139.3333333 Combine like terms: 139.3333333 + -139.3333333 = 0.0000000 0.0000000 + 27.33333333x + x2 = 0 + -139.3333333 27.33333333x + x2 = 0 + -139.3333333 Combine like terms: 0 + -139.3333333 = -139.3333333 27.33333333x + x2 = -139.3333333 The x term is 27.33333333x. Take half its coefficient (13.66666667). Square it (186.7777779) and add it to both sides. Add '186.7777779' to each side of the equation. 27.33333333x + 186.7777779 + x2 = -139.3333333 + 186.7777779 Reorder the terms: 186.7777779 + 27.33333333x + x2 = -139.3333333 + 186.7777779 Combine like terms: -139.3333333 + 186.7777779 = 47.4444446 186.7777779 + 27.33333333x + x2 = 47.4444446 Factor a perfect square on the left side: (x + 13.66666667)(x + 13.66666667) = 47.4444446 Calculate the square root of the right side: 6.887992785 Break this problem into two subproblems by setting (x + 13.66666667) equal to 6.887992785 and -6.887992785.Subproblem 1
x + 13.66666667 = 6.887992785 Simplifying x + 13.66666667 = 6.887992785 Reorder the terms: 13.66666667 + x = 6.887992785 Solving 13.66666667 + x = 6.887992785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.66666667' to each side of the equation. 13.66666667 + -13.66666667 + x = 6.887992785 + -13.66666667 Combine like terms: 13.66666667 + -13.66666667 = 0.00000000 0.00000000 + x = 6.887992785 + -13.66666667 x = 6.887992785 + -13.66666667 Combine like terms: 6.887992785 + -13.66666667 = -6.778673885 x = -6.778673885 Simplifying x = -6.778673885Subproblem 2
x + 13.66666667 = -6.887992785 Simplifying x + 13.66666667 = -6.887992785 Reorder the terms: 13.66666667 + x = -6.887992785 Solving 13.66666667 + x = -6.887992785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.66666667' to each side of the equation. 13.66666667 + -13.66666667 + x = -6.887992785 + -13.66666667 Combine like terms: 13.66666667 + -13.66666667 = 0.00000000 0.00000000 + x = -6.887992785 + -13.66666667 x = -6.887992785 + -13.66666667 Combine like terms: -6.887992785 + -13.66666667 = -20.554659455 x = -20.554659455 Simplifying x = -20.554659455Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.778673885, -20.554659455}
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