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Simplifying (4x + -5)(2x + 17) = 360 Reorder the terms: (-5 + 4x)(2x + 17) = 360 Reorder the terms: (-5 + 4x)(17 + 2x) = 360 Multiply (-5 + 4x) * (17 + 2x) (-5(17 + 2x) + 4x * (17 + 2x)) = 360 ((17 * -5 + 2x * -5) + 4x * (17 + 2x)) = 360 ((-85 + -10x) + 4x * (17 + 2x)) = 360 (-85 + -10x + (17 * 4x + 2x * 4x)) = 360 (-85 + -10x + (68x + 8x2)) = 360 Combine like terms: -10x + 68x = 58x (-85 + 58x + 8x2) = 360 Solving -85 + 58x + 8x2 = 360 Solving for variable 'x'. Reorder the terms: -85 + -360 + 58x + 8x2 = 360 + -360 Combine like terms: -85 + -360 = -445 -445 + 58x + 8x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -445 + 58x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -55.625 + 7.25x + x2 = 0 Move the constant term to the right: Add '55.625' to each side of the equation. -55.625 + 7.25x + 55.625 + x2 = 0 + 55.625 Reorder the terms: -55.625 + 55.625 + 7.25x + x2 = 0 + 55.625 Combine like terms: -55.625 + 55.625 = 0.000 0.000 + 7.25x + x2 = 0 + 55.625 7.25x + x2 = 0 + 55.625 Combine like terms: 0 + 55.625 = 55.625 7.25x + x2 = 55.625 The x term is 7.25x. Take half its coefficient (3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. 7.25x + 13.140625 + x2 = 55.625 + 13.140625 Reorder the terms: 13.140625 + 7.25x + x2 = 55.625 + 13.140625 Combine like terms: 55.625 + 13.140625 = 68.765625 13.140625 + 7.25x + x2 = 68.765625 Factor a perfect square on the left side: (x + 3.625)(x + 3.625) = 68.765625 Calculate the square root of the right side: 8.292504145 Break this problem into two subproblems by setting (x + 3.625) equal to 8.292504145 and -8.292504145.Subproblem 1
x + 3.625 = 8.292504145 Simplifying x + 3.625 = 8.292504145 Reorder the terms: 3.625 + x = 8.292504145 Solving 3.625 + x = 8.292504145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = 8.292504145 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = 8.292504145 + -3.625 x = 8.292504145 + -3.625 Combine like terms: 8.292504145 + -3.625 = 4.667504145 x = 4.667504145 Simplifying x = 4.667504145Subproblem 2
x + 3.625 = -8.292504145 Simplifying x + 3.625 = -8.292504145 Reorder the terms: 3.625 + x = -8.292504145 Solving 3.625 + x = -8.292504145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.625' to each side of the equation. 3.625 + -3.625 + x = -8.292504145 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + x = -8.292504145 + -3.625 x = -8.292504145 + -3.625 Combine like terms: -8.292504145 + -3.625 = -11.917504145 x = -11.917504145 Simplifying x = -11.917504145Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.667504145, -11.917504145}
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