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Simplifying (75x2) + 4825.4862x + -1206371.579 = 0 Reorder the terms: -1206371.579 + 4825.4862x + (75x2) = 0 Solving -1206371.579 + 4825.4862x + (75x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. -16084.95439 + 64.339816x + x2 = 0 Move the constant term to the right: Add '16084.95439' to each side of the equation. -16084.95439 + 64.339816x + 16084.95439 + x2 = 0 + 16084.95439 Reorder the terms: -16084.95439 + 16084.95439 + 64.339816x + x2 = 0 + 16084.95439 Combine like terms: -16084.95439 + 16084.95439 = 0.00000 0.00000 + 64.339816x + x2 = 0 + 16084.95439 64.339816x + x2 = 0 + 16084.95439 Combine like terms: 0 + 16084.95439 = 16084.95439 64.339816x + x2 = 16084.95439 The x term is 64.339816x. Take half its coefficient (32.169908). Square it (1034.902981) and add it to both sides. Add '1034.902981' to each side of the equation. 64.339816x + 1034.902981 + x2 = 16084.95439 + 1034.902981 Reorder the terms: 1034.902981 + 64.339816x + x2 = 16084.95439 + 1034.902981 Combine like terms: 16084.95439 + 1034.902981 = 17119.857371 1034.902981 + 64.339816x + x2 = 17119.857371 Factor a perfect square on the left side: ((x) + 32.169908)((x) + 32.169908) = 17119.857371 Calculate the square root of the right side: 130.842872832 Break this problem into two subproblems by setting ((x) + 32.169908) equal to 130.842872832 and -130.842872832.Subproblem 1
(x) + 32.169908 = 130.842872832 Simplifying (x) + 32.169908 = 130.842872832 x + 32.169908 = 130.842872832 Reorder the terms: 32.169908 + x = 130.842872832 Solving 32.169908 + x = 130.842872832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.169908' to each side of the equation. 32.169908 + -32.169908 + x = 130.842872832 + -32.169908 Combine like terms: 32.169908 + -32.169908 = 0.000000 0.000000 + x = 130.842872832 + -32.169908 x = 130.842872832 + -32.169908 Combine like terms: 130.842872832 + -32.169908 = 98.672964832 x = 98.672964832 Simplifying x = 98.672964832Subproblem 2
(x) + 32.169908 = -130.842872832 Simplifying (x) + 32.169908 = -130.842872832 x + 32.169908 = -130.842872832 Reorder the terms: 32.169908 + x = -130.842872832 Solving 32.169908 + x = -130.842872832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32.169908' to each side of the equation. 32.169908 + -32.169908 + x = -130.842872832 + -32.169908 Combine like terms: 32.169908 + -32.169908 = 0.000000 0.000000 + x = -130.842872832 + -32.169908 x = -130.842872832 + -32.169908 Combine like terms: -130.842872832 + -32.169908 = -163.012780832 x = -163.012780832 Simplifying x = -163.012780832Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.672964832, -163.012780832}
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