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Simplifying x2 + 17x = -5 Reorder the terms: 17x + x2 = -5 Solving 17x + x2 = -5 Solving for variable 'x'. Reorder the terms: 5 + 17x + x2 = -5 + 5 Combine like terms: -5 + 5 = 0 5 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 17x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 17x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 17x + x2 = 0 + -5 17x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 17x + x2 = -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 = -5 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -5 + 72.25 Combine like terms: -5 + 72.25 = 67.25 72.25 + 17x + x2 = 67.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (x + 8.5) equal to 8.200609733 and -8.200609733.Subproblem 1
x + 8.5 = 8.200609733 Simplifying x + 8.5 = 8.200609733 Reorder the terms: 8.5 + x = 8.200609733 Solving 8.5 + x = 8.200609733 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 = 8.200609733 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 8.200609733 + -8.5 x = 8.200609733 + -8.5 Combine like terms: 8.200609733 + -8.5 = -0.299390267 x = -0.299390267 Simplifying x = -0.299390267Subproblem 2
x + 8.5 = -8.200609733 Simplifying x + 8.5 = -8.200609733 Reorder the terms: 8.5 + x = -8.200609733 Solving 8.5 + x = -8.200609733 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 = -8.200609733 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -8.200609733 + -8.5 x = -8.200609733 + -8.5 Combine like terms: -8.200609733 + -8.5 = -16.700609733 x = -16.700609733 Simplifying x = -16.700609733Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.299390267, -16.700609733}
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