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Simplifying (-1x(-1x)) + 30x + 17 = 8x + 102 Remove parenthesis around (-1x) (-1x * -1x) + 30x + 17 = 8x + 102 Reorder the terms for easier multiplication: (-1 * -1x * x) + 30x + 17 = 8x + 102 Multiply -1 * -1 (1x * x) + 30x + 17 = 8x + 102 Multiply x * x (1x2) + 30x + 17 = 8x + 102 Reorder the terms: 17 + 30x + (1x2) = 8x + 102 Reorder the terms: 17 + 30x + (1x2) = 102 + 8x Solving 17 + 30x + (1x2) = 102 + 8x Solving for variable 'x'. Reorder the terms: 17 + -102 + 30x + -8x + (1x2) = 102 + 8x + -102 + -8x Combine like terms: 17 + -102 = -85 -85 + 30x + -8x + (1x2) = 102 + 8x + -102 + -8x Combine like terms: 30x + -8x = 22x -85 + 22x + (1x2) = 102 + 8x + -102 + -8x Reorder the terms: -85 + 22x + (1x2) = 102 + -102 + 8x + -8x Combine like terms: 102 + -102 = 0 -85 + 22x + (1x2) = 0 + 8x + -8x -85 + 22x + (1x2) = 8x + -8x Combine like terms: 8x + -8x = 0 -85 + 22x + (1x2) = 0 Begin completing the square. Move the constant term to the right: Add '85' to each side of the equation. -85 + 22x + 85 + (x2) = 0 + 85 -85 + 22x + 85 + x2 = 0 + 85 Reorder the terms: -85 + 85 + 22x + x2 = 0 + 85 Combine like terms: -85 + 85 = 0 0 + 22x + x2 = 0 + 85 22x + x2 = 0 + 85 Combine like terms: 0 + 85 = 85 22x + x2 = 85 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = 85 + 121 Reorder the terms: 121 + 22x + x2 = 85 + 121 Combine like terms: 85 + 121 = 206 121 + 22x + x2 = 206 Factor a perfect square on the left side: ((x) + 11)((x) + 11) = 206 Calculate the square root of the right side: 14.352700094 Break this problem into two subproblems by setting ((x) + 11) equal to 14.352700094 and -14.352700094.Subproblem 1
(x) + 11 = 14.352700094 Simplifying (x) + 11 = 14.352700094 x + 11 = 14.352700094 Reorder the terms: 11 + x = 14.352700094 Solving 11 + x = 14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 14.352700094 + -11 Combine like terms: 11 + -11 = 0 0 + x = 14.352700094 + -11 x = 14.352700094 + -11 Combine like terms: 14.352700094 + -11 = 3.352700094 x = 3.352700094 Simplifying x = 3.352700094Subproblem 2
(x) + 11 = -14.352700094 Simplifying (x) + 11 = -14.352700094 x + 11 = -14.352700094 Reorder the terms: 11 + x = -14.352700094 Solving 11 + x = -14.352700094 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -14.352700094 + -11 Combine like terms: 11 + -11 = 0 0 + x = -14.352700094 + -11 x = -14.352700094 + -11 Combine like terms: -14.352700094 + -11 = -25.352700094 x = -25.352700094 Simplifying x = -25.352700094Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.352700094, -25.352700094}
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