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Simplifying 2x2 + 17x + -360 = 0 Reorder the terms: -360 + 17x + 2x2 = 0 Solving -360 + 17x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -180 + 8.5x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 8.5x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 8.5x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 8.5x + x2 = 0 + 180 8.5x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 8.5x + x2 = 180 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = 180 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = 180 + 18.0625 Combine like terms: 180 + 18.0625 = 198.0625 18.0625 + 8.5x + x2 = 198.0625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 198.0625 Calculate the square root of the right side: 14.073467945 Break this problem into two subproblems by setting (x + 4.25) equal to 14.073467945 and -14.073467945.Subproblem 1
x + 4.25 = 14.073467945 Simplifying x + 4.25 = 14.073467945 Reorder the terms: 4.25 + x = 14.073467945 Solving 4.25 + x = 14.073467945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 14.073467945 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 14.073467945 + -4.25 x = 14.073467945 + -4.25 Combine like terms: 14.073467945 + -4.25 = 9.823467945 x = 9.823467945 Simplifying x = 9.823467945Subproblem 2
x + 4.25 = -14.073467945 Simplifying x + 4.25 = -14.073467945 Reorder the terms: 4.25 + x = -14.073467945 Solving 4.25 + x = -14.073467945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -14.073467945 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -14.073467945 + -4.25 x = -14.073467945 + -4.25 Combine like terms: -14.073467945 + -4.25 = -18.323467945 x = -18.323467945 Simplifying x = -18.323467945Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.823467945, -18.323467945}
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