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Simplifying x2 + 17x + -81 = 0 Reorder the terms: -81 + 17x + x2 = 0 Solving -81 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 17x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 17x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 17x + x2 = 0 + 81 17x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 17x + x2 = 81 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 = 81 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 81 + 72.25 Combine like terms: 81 + 72.25 = 153.25 72.25 + 17x + x2 = 153.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 153.25 Calculate the square root of the right side: 12.379418403 Break this problem into two subproblems by setting (x + 8.5) equal to 12.379418403 and -12.379418403.Subproblem 1
x + 8.5 = 12.379418403 Simplifying x + 8.5 = 12.379418403 Reorder the terms: 8.5 + x = 12.379418403 Solving 8.5 + x = 12.379418403 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 = 12.379418403 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 12.379418403 + -8.5 x = 12.379418403 + -8.5 Combine like terms: 12.379418403 + -8.5 = 3.879418403 x = 3.879418403 Simplifying x = 3.879418403Subproblem 2
x + 8.5 = -12.379418403 Simplifying x + 8.5 = -12.379418403 Reorder the terms: 8.5 + x = -12.379418403 Solving 8.5 + x = -12.379418403 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 = -12.379418403 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -12.379418403 + -8.5 x = -12.379418403 + -8.5 Combine like terms: -12.379418403 + -8.5 = -20.879418403 x = -20.879418403 Simplifying x = -20.879418403Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.879418403, -20.879418403}
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