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Simplifying x2 + 17x + 1 = 0 Reorder the terms: 1 + 17x + x2 = 0 Solving 1 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 17x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 17x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 17x + x2 = 0 + -1 17x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 17x + x2 = -1 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 = -1 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -1 + 72.25 Combine like terms: -1 + 72.25 = 71.25 72.25 + 17x + x2 = 71.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (x + 8.5) equal to 8.440971508 and -8.440971508.Subproblem 1
x + 8.5 = 8.440971508 Simplifying x + 8.5 = 8.440971508 Reorder the terms: 8.5 + x = 8.440971508 Solving 8.5 + x = 8.440971508 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 = 8.440971508 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 8.440971508 + -8.5 x = 8.440971508 + -8.5 Combine like terms: 8.440971508 + -8.5 = -0.059028492 x = -0.059028492 Simplifying x = -0.059028492Subproblem 2
x + 8.5 = -8.440971508 Simplifying x + 8.5 = -8.440971508 Reorder the terms: 8.5 + x = -8.440971508 Solving 8.5 + x = -8.440971508 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 = -8.440971508 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -8.440971508 + -8.5 x = -8.440971508 + -8.5 Combine like terms: -8.440971508 + -8.5 = -16.940971508 x = -16.940971508 Simplifying x = -16.940971508Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.059028492, -16.940971508}
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