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Simplifying x2 + 17x + 8 = -3 Reorder the terms: 8 + 17x + x2 = -3 Solving 8 + 17x + x2 = -3 Solving for variable 'x'. Reorder the terms: 8 + 3 + 17x + x2 = -3 + 3 Combine like terms: 8 + 3 = 11 11 + 17x + x2 = -3 + 3 Combine like terms: -3 + 3 = 0 11 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + 17x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + 17x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 17x + x2 = 0 + -11 17x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 17x + x2 = -11 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 = -11 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -11 + 72.25 Combine like terms: -11 + 72.25 = 61.25 72.25 + 17x + x2 = 61.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 61.25 Calculate the square root of the right side: 7.826237921 Break this problem into two subproblems by setting (x + 8.5) equal to 7.826237921 and -7.826237921.Subproblem 1
x + 8.5 = 7.826237921 Simplifying x + 8.5 = 7.826237921 Reorder the terms: 8.5 + x = 7.826237921 Solving 8.5 + x = 7.826237921 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 = 7.826237921 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 7.826237921 + -8.5 x = 7.826237921 + -8.5 Combine like terms: 7.826237921 + -8.5 = -0.673762079 x = -0.673762079 Simplifying x = -0.673762079Subproblem 2
x + 8.5 = -7.826237921 Simplifying x + 8.5 = -7.826237921 Reorder the terms: 8.5 + x = -7.826237921 Solving 8.5 + x = -7.826237921 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 = -7.826237921 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -7.826237921 + -8.5 x = -7.826237921 + -8.5 Combine like terms: -7.826237921 + -8.5 = -16.326237921 x = -16.326237921 Simplifying x = -16.326237921Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.673762079, -16.326237921}
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