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Simplifying 2x2 + -59x + 360 = 0 Reorder the terms: 360 + -59x + 2x2 = 0 Solving 360 + -59x + 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 + -29.5x + x2 = 0 Move the constant term to the right: Add '-180' to each side of the equation. 180 + -29.5x + -180 + x2 = 0 + -180 Reorder the terms: 180 + -180 + -29.5x + x2 = 0 + -180 Combine like terms: 180 + -180 = 0 0 + -29.5x + x2 = 0 + -180 -29.5x + x2 = 0 + -180 Combine like terms: 0 + -180 = -180 -29.5x + x2 = -180 The x term is -29.5x. Take half its coefficient (-14.75). Square it (217.5625) and add it to both sides. Add '217.5625' to each side of the equation. -29.5x + 217.5625 + x2 = -180 + 217.5625 Reorder the terms: 217.5625 + -29.5x + x2 = -180 + 217.5625 Combine like terms: -180 + 217.5625 = 37.5625 217.5625 + -29.5x + x2 = 37.5625 Factor a perfect square on the left side: (x + -14.75)(x + -14.75) = 37.5625 Calculate the square root of the right side: 6.128825336 Break this problem into two subproblems by setting (x + -14.75) equal to 6.128825336 and -6.128825336.Subproblem 1
x + -14.75 = 6.128825336 Simplifying x + -14.75 = 6.128825336 Reorder the terms: -14.75 + x = 6.128825336 Solving -14.75 + x = 6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = 6.128825336 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = 6.128825336 + 14.75 x = 6.128825336 + 14.75 Combine like terms: 6.128825336 + 14.75 = 20.878825336 x = 20.878825336 Simplifying x = 20.878825336Subproblem 2
x + -14.75 = -6.128825336 Simplifying x + -14.75 = -6.128825336 Reorder the terms: -14.75 + x = -6.128825336 Solving -14.75 + x = -6.128825336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.75' to each side of the equation. -14.75 + 14.75 + x = -6.128825336 + 14.75 Combine like terms: -14.75 + 14.75 = 0.00 0.00 + x = -6.128825336 + 14.75 x = -6.128825336 + 14.75 Combine like terms: -6.128825336 + 14.75 = 8.621174664 x = 8.621174664 Simplifying x = 8.621174664Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.878825336, 8.621174664}
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