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Simplifying 2x2 = 29.5 + -14.5x Solving 2x2 = 29.5 + -14.5x Solving for variable 'x'. Reorder the terms: -29.5 + 14.5x + 2x2 = 29.5 + -14.5x + -29.5 + 14.5x Reorder the terms: -29.5 + 14.5x + 2x2 = 29.5 + -29.5 + -14.5x + 14.5x Combine like terms: 29.5 + -29.5 = 0.0 -29.5 + 14.5x + 2x2 = 0.0 + -14.5x + 14.5x -29.5 + 14.5x + 2x2 = -14.5x + 14.5x Combine like terms: -14.5x + 14.5x = 0.0 -29.5 + 14.5x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.75 + 7.25x + x2 = 0.0 Move the constant term to the right: Add '14.75' to each side of the equation. -14.75 + 7.25x + 14.75 + x2 = 0.0 + 14.75 Reorder the terms: -14.75 + 14.75 + 7.25x + x2 = 0.0 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + 7.25x + x2 = 0.0 + 14.75 7.25x + x2 = 0.0 + 14.75 Combine like terms: 0.0 + 14.75 = 14.75 7.25x + x2 = 14.75 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = 14.75 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = 14.75 + 13.140625 Combine like terms: 14.75 + 13.140625 = 27.890625 13.140625 + 7.25x + x2 = 27.890625 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = 27.890625 Calculate the square root of the right side: 5.281157544 Break this problem into two subproblems by setting (x + 3.625) equal to 5.281157544 and -5.281157544.Subproblem 1
x + 3.625 = 5.281157544 Simplifying x + 3.625 = 5.281157544 Reorder the terms: 3.625 + x = 5.281157544 Solving 3.625 + x = 5.281157544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = 5.281157544 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 5.281157544 + -3.625 x = 5.281157544 + -3.625 Combine like terms: 5.281157544 + -3.625 = 1.656157544 x = 1.656157544 Simplifying x = 1.656157544Subproblem 2
x + 3.625 = -5.281157544 Simplifying x + 3.625 = -5.281157544 Reorder the terms: 3.625 + x = -5.281157544 Solving 3.625 + x = -5.281157544 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = -5.281157544 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -5.281157544 + -3.625 x = -5.281157544 + -3.625 Combine like terms: -5.281157544 + -3.625 = -8.906157544 x = -8.906157544 Simplifying x = -8.906157544Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.656157544, -8.906157544}
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