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Simplifying 3485x2 + -311107.5x + -18855000 = 0 Reorder the terms: -18855000 + -311107.5x + 3485x2 = 0 Solving -18855000 + -311107.5x + 3485x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3485 the coefficient of the squared term: Divide each side by '3485'. -5410.329986 + -89.27044476x + x2 = 0 Move the constant term to the right: Add '5410.329986' to each side of the equation. -5410.329986 + -89.27044476x + 5410.329986 + x2 = 0 + 5410.329986 Reorder the terms: -5410.329986 + 5410.329986 + -89.27044476x + x2 = 0 + 5410.329986 Combine like terms: -5410.329986 + 5410.329986 = 0.000000 0.000000 + -89.27044476x + x2 = 0 + 5410.329986 -89.27044476x + x2 = 0 + 5410.329986 Combine like terms: 0 + 5410.329986 = 5410.329986 -89.27044476x + x2 = 5410.329986 The x term is -89.27044476x. Take half its coefficient (-44.63522238). Square it (1992.303077) and add it to both sides. Add '1992.303077' to each side of the equation. -89.27044476x + 1992.303077 + x2 = 5410.329986 + 1992.303077 Reorder the terms: 1992.303077 + -89.27044476x + x2 = 5410.329986 + 1992.303077 Combine like terms: 5410.329986 + 1992.303077 = 7402.633063 1992.303077 + -89.27044476x + x2 = 7402.633063 Factor a perfect square on the left side: (x + -44.63522238)(x + -44.63522238) = 7402.633063 Calculate the square root of the right side: 86.038555677 Break this problem into two subproblems by setting (x + -44.63522238) equal to 86.038555677 and -86.038555677.Subproblem 1
x + -44.63522238 = 86.038555677 Simplifying x + -44.63522238 = 86.038555677 Reorder the terms: -44.63522238 + x = 86.038555677 Solving -44.63522238 + x = 86.038555677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.63522238' to each side of the equation. -44.63522238 + 44.63522238 + x = 86.038555677 + 44.63522238 Combine like terms: -44.63522238 + 44.63522238 = 0.00000000 0.00000000 + x = 86.038555677 + 44.63522238 x = 86.038555677 + 44.63522238 Combine like terms: 86.038555677 + 44.63522238 = 130.673778057 x = 130.673778057 Simplifying x = 130.673778057Subproblem 2
x + -44.63522238 = -86.038555677 Simplifying x + -44.63522238 = -86.038555677 Reorder the terms: -44.63522238 + x = -86.038555677 Solving -44.63522238 + x = -86.038555677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.63522238' to each side of the equation. -44.63522238 + 44.63522238 + x = -86.038555677 + 44.63522238 Combine like terms: -44.63522238 + 44.63522238 = 0.00000000 0.00000000 + x = -86.038555677 + 44.63522238 x = -86.038555677 + 44.63522238 Combine like terms: -86.038555677 + 44.63522238 = -41.403333297 x = -41.403333297 Simplifying x = -41.403333297Solution
The solution to the problem is based on the solutions from the subproblems. x = {130.673778057, -41.403333297}
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