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Simplifying -1706682490.35 + 629008.22x + 213.36x2 = 0 Solving -1706682490.35 + 629008.22x + 213.36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 213.36 the coefficient of the squared term: Divide each side by '213.36'. -7999074.289 + 2948.107518x + x2 = 0 Move the constant term to the right: Add '7999074.289' to each side of the equation. -7999074.289 + 2948.107518x + 7999074.289 + x2 = 0 + 7999074.289 Reorder the terms: -7999074.289 + 7999074.289 + 2948.107518x + x2 = 0 + 7999074.289 Combine like terms: -7999074.289 + 7999074.289 = 0.000 0.000 + 2948.107518x + x2 = 0 + 7999074.289 2948.107518x + x2 = 0 + 7999074.289 Combine like terms: 0 + 7999074.289 = 7999074.289 2948.107518x + x2 = 7999074.289 The x term is 2948.107518x. Take half its coefficient (1474.053759). Square it (2172834.484) and add it to both sides. Add '2172834.484' to each side of the equation. 2948.107518x + 2172834.484 + x2 = 7999074.289 + 2172834.484 Reorder the terms: 2172834.484 + 2948.107518x + x2 = 7999074.289 + 2172834.484 Combine like terms: 7999074.289 + 2172834.484 = 10171908.773 2172834.484 + 2948.107518x + x2 = 10171908.773 Factor a perfect square on the left side: (x + 1474.053759)(x + 1474.053759) = 10171908.773 Calculate the square root of the right side: 3189.343000212 Break this problem into two subproblems by setting (x + 1474.053759) equal to 3189.343000212 and -3189.343000212.Subproblem 1
x + 1474.053759 = 3189.343000212 Simplifying x + 1474.053759 = 3189.343000212 Reorder the terms: 1474.053759 + x = 3189.343000212 Solving 1474.053759 + x = 3189.343000212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1474.053759' to each side of the equation. 1474.053759 + -1474.053759 + x = 3189.343000212 + -1474.053759 Combine like terms: 1474.053759 + -1474.053759 = 0.000000 0.000000 + x = 3189.343000212 + -1474.053759 x = 3189.343000212 + -1474.053759 Combine like terms: 3189.343000212 + -1474.053759 = 1715.289241212 x = 1715.289241212 Simplifying x = 1715.289241212Subproblem 2
x + 1474.053759 = -3189.343000212 Simplifying x + 1474.053759 = -3189.343000212 Reorder the terms: 1474.053759 + x = -3189.343000212 Solving 1474.053759 + x = -3189.343000212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1474.053759' to each side of the equation. 1474.053759 + -1474.053759 + x = -3189.343000212 + -1474.053759 Combine like terms: 1474.053759 + -1474.053759 = 0.000000 0.000000 + x = -3189.343000212 + -1474.053759 x = -3189.343000212 + -1474.053759 Combine like terms: -3189.343000212 + -1474.053759 = -4663.396759212 x = -4663.396759212 Simplifying x = -4663.396759212Solution
The solution to the problem is based on the solutions from the subproblems. x = {1715.289241212, -4663.396759212}
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