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Simplifying -22x2 + 515.5x + -2375 = 0 Reorder the terms: -2375 + 515.5x + -22x2 = 0 Solving -2375 + 515.5x + -22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -22 the coefficient of the squared term: Divide each side by '-22'. 107.9545455 + -23.43181818x + x2 = 0 Move the constant term to the right: Add '-107.9545455' to each side of the equation. 107.9545455 + -23.43181818x + -107.9545455 + x2 = 0 + -107.9545455 Reorder the terms: 107.9545455 + -107.9545455 + -23.43181818x + x2 = 0 + -107.9545455 Combine like terms: 107.9545455 + -107.9545455 = 0.0000000 0.0000000 + -23.43181818x + x2 = 0 + -107.9545455 -23.43181818x + x2 = 0 + -107.9545455 Combine like terms: 0 + -107.9545455 = -107.9545455 -23.43181818x + x2 = -107.9545455 The x term is -23.43181818x. Take half its coefficient (-11.71590909). Square it (137.2625258) and add it to both sides. Add '137.2625258' to each side of the equation. -23.43181818x + 137.2625258 + x2 = -107.9545455 + 137.2625258 Reorder the terms: 137.2625258 + -23.43181818x + x2 = -107.9545455 + 137.2625258 Combine like terms: -107.9545455 + 137.2625258 = 29.3079803 137.2625258 + -23.43181818x + x2 = 29.3079803 Factor a perfect square on the left side: (x + -11.71590909)(x + -11.71590909) = 29.3079803 Calculate the square root of the right side: 5.41368454 Break this problem into two subproblems by setting (x + -11.71590909) equal to 5.41368454 and -5.41368454.Subproblem 1
x + -11.71590909 = 5.41368454 Simplifying x + -11.71590909 = 5.41368454 Reorder the terms: -11.71590909 + x = 5.41368454 Solving -11.71590909 + x = 5.41368454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.71590909' to each side of the equation. -11.71590909 + 11.71590909 + x = 5.41368454 + 11.71590909 Combine like terms: -11.71590909 + 11.71590909 = 0.00000000 0.00000000 + x = 5.41368454 + 11.71590909 x = 5.41368454 + 11.71590909 Combine like terms: 5.41368454 + 11.71590909 = 17.12959363 x = 17.12959363 Simplifying x = 17.12959363Subproblem 2
x + -11.71590909 = -5.41368454 Simplifying x + -11.71590909 = -5.41368454 Reorder the terms: -11.71590909 + x = -5.41368454 Solving -11.71590909 + x = -5.41368454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.71590909' to each side of the equation. -11.71590909 + 11.71590909 + x = -5.41368454 + 11.71590909 Combine like terms: -11.71590909 + 11.71590909 = 0.00000000 0.00000000 + x = -5.41368454 + 11.71590909 x = -5.41368454 + 11.71590909 Combine like terms: -5.41368454 + 11.71590909 = 6.30222455 x = 6.30222455 Simplifying x = 6.30222455Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.12959363, 6.30222455}
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