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Simplifying 8x2 + 134x + 245 = 0 Reorder the terms: 245 + 134x + 8x2 = 0 Solving 245 + 134x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 30.625 + 16.75x + x2 = 0 Move the constant term to the right: Add '-30.625' to each side of the equation. 30.625 + 16.75x + -30.625 + x2 = 0 + -30.625 Reorder the terms: 30.625 + -30.625 + 16.75x + x2 = 0 + -30.625 Combine like terms: 30.625 + -30.625 = 0.000 0.000 + 16.75x + x2 = 0 + -30.625 16.75x + x2 = 0 + -30.625 Combine like terms: 0 + -30.625 = -30.625 16.75x + x2 = -30.625 The x term is 16.75x. Take half its coefficient (8.375). Square it (70.140625) and add it to both sides. Add '70.140625' to each side of the equation. 16.75x + 70.140625 + x2 = -30.625 + 70.140625 Reorder the terms: 70.140625 + 16.75x + x2 = -30.625 + 70.140625 Combine like terms: -30.625 + 70.140625 = 39.515625 70.140625 + 16.75x + x2 = 39.515625 Factor a perfect square on the left side: (x + 8.375)(x + 8.375) = 39.515625 Calculate the square root of the right side: 6.28614548 Break this problem into two subproblems by setting (x + 8.375) equal to 6.28614548 and -6.28614548.Subproblem 1
x + 8.375 = 6.28614548 Simplifying x + 8.375 = 6.28614548 Reorder the terms: 8.375 + x = 6.28614548 Solving 8.375 + x = 6.28614548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = 6.28614548 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = 6.28614548 + -8.375 x = 6.28614548 + -8.375 Combine like terms: 6.28614548 + -8.375 = -2.08885452 x = -2.08885452 Simplifying x = -2.08885452Subproblem 2
x + 8.375 = -6.28614548 Simplifying x + 8.375 = -6.28614548 Reorder the terms: 8.375 + x = -6.28614548 Solving 8.375 + x = -6.28614548 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = -6.28614548 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = -6.28614548 + -8.375 x = -6.28614548 + -8.375 Combine like terms: -6.28614548 + -8.375 = -14.66114548 x = -14.66114548 Simplifying x = -14.66114548Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.08885452, -14.66114548}
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