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Simplifying x = -16x2 + 1280x + -11200 Reorder the terms: x = -11200 + 1280x + -16x2 Solving x = -11200 + 1280x + -16x2 Solving for variable 'x'. Reorder the terms: 11200 + x + -1280x + 16x2 = -11200 + 1280x + -16x2 + 11200 + -1280x + 16x2 Combine like terms: x + -1280x = -1279x 11200 + -1279x + 16x2 = -11200 + 1280x + -16x2 + 11200 + -1280x + 16x2 Reorder the terms: 11200 + -1279x + 16x2 = -11200 + 11200 + 1280x + -1280x + -16x2 + 16x2 Combine like terms: -11200 + 11200 = 0 11200 + -1279x + 16x2 = 0 + 1280x + -1280x + -16x2 + 16x2 11200 + -1279x + 16x2 = 1280x + -1280x + -16x2 + 16x2 Combine like terms: 1280x + -1280x = 0 11200 + -1279x + 16x2 = 0 + -16x2 + 16x2 11200 + -1279x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 11200 + -1279x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 700 + -79.9375x + x2 = 0 Move the constant term to the right: Add '-700' to each side of the equation. 700 + -79.9375x + -700 + x2 = 0 + -700 Reorder the terms: 700 + -700 + -79.9375x + x2 = 0 + -700 Combine like terms: 700 + -700 = 0 0 + -79.9375x + x2 = 0 + -700 -79.9375x + x2 = 0 + -700 Combine like terms: 0 + -700 = -700 -79.9375x + x2 = -700 The x term is -79.9375x. Take half its coefficient (-39.96875). Square it (1597.500977) and add it to both sides. Add '1597.500977' to each side of the equation. -79.9375x + 1597.500977 + x2 = -700 + 1597.500977 Reorder the terms: 1597.500977 + -79.9375x + x2 = -700 + 1597.500977 Combine like terms: -700 + 1597.500977 = 897.500977 1597.500977 + -79.9375x + x2 = 897.500977 Factor a perfect square on the left side: (x + -39.96875)(x + -39.96875) = 897.500977 Calculate the square root of the right side: 29.958320664 Break this problem into two subproblems by setting (x + -39.96875) equal to 29.958320664 and -29.958320664.Subproblem 1
x + -39.96875 = 29.958320664 Simplifying x + -39.96875 = 29.958320664 Reorder the terms: -39.96875 + x = 29.958320664 Solving -39.96875 + x = 29.958320664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39.96875' to each side of the equation. -39.96875 + 39.96875 + x = 29.958320664 + 39.96875 Combine like terms: -39.96875 + 39.96875 = 0.00000 0.00000 + x = 29.958320664 + 39.96875 x = 29.958320664 + 39.96875 Combine like terms: 29.958320664 + 39.96875 = 69.927070664 x = 69.927070664 Simplifying x = 69.927070664Subproblem 2
x + -39.96875 = -29.958320664 Simplifying x + -39.96875 = -29.958320664 Reorder the terms: -39.96875 + x = -29.958320664 Solving -39.96875 + x = -29.958320664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39.96875' to each side of the equation. -39.96875 + 39.96875 + x = -29.958320664 + 39.96875 Combine like terms: -39.96875 + 39.96875 = 0.00000 0.00000 + x = -29.958320664 + 39.96875 x = -29.958320664 + 39.96875 Combine like terms: -29.958320664 + 39.96875 = 10.010429336 x = 10.010429336 Simplifying x = 10.010429336Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.927070664, 10.010429336}
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