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Simplifying -1x2 + 3720x + 17954 = 0 Reorder the terms: 17954 + 3720x + -1x2 = 0 Solving 17954 + 3720x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17954 + -3720x + x2 = 0 Move the constant term to the right: Add '17954' to each side of the equation. -17954 + -3720x + 17954 + x2 = 0 + 17954 Reorder the terms: -17954 + 17954 + -3720x + x2 = 0 + 17954 Combine like terms: -17954 + 17954 = 0 0 + -3720x + x2 = 0 + 17954 -3720x + x2 = 0 + 17954 Combine like terms: 0 + 17954 = 17954 -3720x + x2 = 17954 The x term is -3720x. Take half its coefficient (-1860). Square it (3459600) and add it to both sides. Add '3459600' to each side of the equation. -3720x + 3459600 + x2 = 17954 + 3459600 Reorder the terms: 3459600 + -3720x + x2 = 17954 + 3459600 Combine like terms: 17954 + 3459600 = 3477554 3459600 + -3720x + x2 = 3477554 Factor a perfect square on the left side: (x + -1860)(x + -1860) = 3477554 Calculate the square root of the right side: 1864.820098562 Break this problem into two subproblems by setting (x + -1860) equal to 1864.820098562 and -1864.820098562.Subproblem 1
x + -1860 = 1864.820098562 Simplifying x + -1860 = 1864.820098562 Reorder the terms: -1860 + x = 1864.820098562 Solving -1860 + x = 1864.820098562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1860' to each side of the equation. -1860 + 1860 + x = 1864.820098562 + 1860 Combine like terms: -1860 + 1860 = 0 0 + x = 1864.820098562 + 1860 x = 1864.820098562 + 1860 Combine like terms: 1864.820098562 + 1860 = 3724.820098562 x = 3724.820098562 Simplifying x = 3724.820098562Subproblem 2
x + -1860 = -1864.820098562 Simplifying x + -1860 = -1864.820098562 Reorder the terms: -1860 + x = -1864.820098562 Solving -1860 + x = -1864.820098562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1860' to each side of the equation. -1860 + 1860 + x = -1864.820098562 + 1860 Combine like terms: -1860 + 1860 = 0 0 + x = -1864.820098562 + 1860 x = -1864.820098562 + 1860 Combine like terms: -1864.820098562 + 1860 = -4.820098562 x = -4.820098562 Simplifying x = -4.820098562Solution
The solution to the problem is based on the solutions from the subproblems. x = {3724.820098562, -4.820098562}
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