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Simplifying 58x + -0.83x2 = 1 Solving 58x + -0.83x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 58x + -0.83x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 58x + -0.83x2 = 0 Begin completing the square. Divide all terms by -0.83 the coefficient of the squared term: Divide each side by '-0.83'. 1.204819277 + -69.87951807x + x2 = 0 Move the constant term to the right: Add '-1.204819277' to each side of the equation. 1.204819277 + -69.87951807x + -1.204819277 + x2 = 0 + -1.204819277 Reorder the terms: 1.204819277 + -1.204819277 + -69.87951807x + x2 = 0 + -1.204819277 Combine like terms: 1.204819277 + -1.204819277 = 0.000000000 0.000000000 + -69.87951807x + x2 = 0 + -1.204819277 -69.87951807x + x2 = 0 + -1.204819277 Combine like terms: 0 + -1.204819277 = -1.204819277 -69.87951807x + x2 = -1.204819277 The x term is -69.87951807x. Take half its coefficient (-34.93975904). Square it (1220.786762) and add it to both sides. Add '1220.786762' to each side of the equation. -69.87951807x + 1220.786762 + x2 = -1.204819277 + 1220.786762 Reorder the terms: 1220.786762 + -69.87951807x + x2 = -1.204819277 + 1220.786762 Combine like terms: -1.204819277 + 1220.786762 = 1219.581942723 1220.786762 + -69.87951807x + x2 = 1219.581942723 Factor a perfect square on the left side: (x + -34.93975904)(x + -34.93975904) = 1219.581942723 Calculate the square root of the right side: 34.922513408 Break this problem into two subproblems by setting (x + -34.93975904) equal to 34.922513408 and -34.922513408.Subproblem 1
x + -34.93975904 = 34.922513408 Simplifying x + -34.93975904 = 34.922513408 Reorder the terms: -34.93975904 + x = 34.922513408 Solving -34.93975904 + x = 34.922513408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34.93975904' to each side of the equation. -34.93975904 + 34.93975904 + x = 34.922513408 + 34.93975904 Combine like terms: -34.93975904 + 34.93975904 = 0.00000000 0.00000000 + x = 34.922513408 + 34.93975904 x = 34.922513408 + 34.93975904 Combine like terms: 34.922513408 + 34.93975904 = 69.862272448 x = 69.862272448 Simplifying x = 69.862272448Subproblem 2
x + -34.93975904 = -34.922513408 Simplifying x + -34.93975904 = -34.922513408 Reorder the terms: -34.93975904 + x = -34.922513408 Solving -34.93975904 + x = -34.922513408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '34.93975904' to each side of the equation. -34.93975904 + 34.93975904 + x = -34.922513408 + 34.93975904 Combine like terms: -34.93975904 + 34.93975904 = 0.00000000 0.00000000 + x = -34.922513408 + 34.93975904 x = -34.922513408 + 34.93975904 Combine like terms: -34.922513408 + 34.93975904 = 0.017245632 x = 0.017245632 Simplifying x = 0.017245632Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.862272448, 0.017245632}
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