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Simplifying x2 + 17x = 2040 Reorder the terms: 17x + x2 = 2040 Solving 17x + x2 = 2040 Solving for variable 'x'. Reorder the terms: -2040 + 17x + x2 = 2040 + -2040 Combine like terms: 2040 + -2040 = 0 -2040 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2040' to each side of the equation. -2040 + 17x + 2040 + x2 = 0 + 2040 Reorder the terms: -2040 + 2040 + 17x + x2 = 0 + 2040 Combine like terms: -2040 + 2040 = 0 0 + 17x + x2 = 0 + 2040 17x + x2 = 0 + 2040 Combine like terms: 0 + 2040 = 2040 17x + x2 = 2040 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 = 2040 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 2040 + 72.25 Combine like terms: 2040 + 72.25 = 2112.25 72.25 + 17x + x2 = 2112.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 2112.25 Calculate the square root of the right side: 45.959221055 Break this problem into two subproblems by setting (x + 8.5) equal to 45.959221055 and -45.959221055.Subproblem 1
x + 8.5 = 45.959221055 Simplifying x + 8.5 = 45.959221055 Reorder the terms: 8.5 + x = 45.959221055 Solving 8.5 + x = 45.959221055 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 = 45.959221055 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 45.959221055 + -8.5 x = 45.959221055 + -8.5 Combine like terms: 45.959221055 + -8.5 = 37.459221055 x = 37.459221055 Simplifying x = 37.459221055Subproblem 2
x + 8.5 = -45.959221055 Simplifying x + 8.5 = -45.959221055 Reorder the terms: 8.5 + x = -45.959221055 Solving 8.5 + x = -45.959221055 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 = -45.959221055 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -45.959221055 + -8.5 x = -45.959221055 + -8.5 Combine like terms: -45.959221055 + -8.5 = -54.459221055 x = -54.459221055 Simplifying x = -54.459221055Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.459221055, -54.459221055}
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