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Simplifying 0 = -2x2 + -34x + 289 Reorder the terms: 0 = 289 + -34x + -2x2 Solving 0 = 289 + -34x + -2x2 Solving for variable 'x'. Combine like terms: 0 + -289 = -289 -289 + 34x + 2x2 = 289 + -34x + -2x2 + -289 + 34x + 2x2 Reorder the terms: -289 + 34x + 2x2 = 289 + -289 + -34x + 34x + -2x2 + 2x2 Combine like terms: 289 + -289 = 0 -289 + 34x + 2x2 = 0 + -34x + 34x + -2x2 + 2x2 -289 + 34x + 2x2 = -34x + 34x + -2x2 + 2x2 Combine like terms: -34x + 34x = 0 -289 + 34x + 2x2 = 0 + -2x2 + 2x2 -289 + 34x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -289 + 34x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -144.5 + 17x + x2 = 0 Move the constant term to the right: Add '144.5' to each side of the equation. -144.5 + 17x + 144.5 + x2 = 0 + 144.5 Reorder the terms: -144.5 + 144.5 + 17x + x2 = 0 + 144.5 Combine like terms: -144.5 + 144.5 = 0.0 0.0 + 17x + x2 = 0 + 144.5 17x + x2 = 0 + 144.5 Combine like terms: 0 + 144.5 = 144.5 17x + x2 = 144.5 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 144.5 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 144.5 + 72.25 Combine like terms: 144.5 + 72.25 = 216.75 72.25 + 17x + x2 = 216.75 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 216.75 Calculate the square root of the right side: 14.722431864 Break this problem into two subproblems by setting (x + 8.5) equal to 14.722431864 and -14.722431864.Subproblem 1
x + 8.5 = 14.722431864 Simplifying x + 8.5 = 14.722431864 Reorder the terms: 8.5 + x = 14.722431864 Solving 8.5 + x = 14.722431864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 14.722431864 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 14.722431864 + -8.5 x = 14.722431864 + -8.5 Combine like terms: 14.722431864 + -8.5 = 6.222431864 x = 6.222431864 Simplifying x = 6.222431864Subproblem 2
x + 8.5 = -14.722431864 Simplifying x + 8.5 = -14.722431864 Reorder the terms: 8.5 + x = -14.722431864 Solving 8.5 + x = -14.722431864 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -14.722431864 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -14.722431864 + -8.5 x = -14.722431864 + -8.5 Combine like terms: -14.722431864 + -8.5 = -23.222431864 x = -23.222431864 Simplifying x = -23.222431864Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.222431864, -23.222431864}
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