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Simplifying 3200x + -1x2 = 3200 Solving 3200x + -1x2 = 3200 Solving for variable 'x'. Reorder the terms: -3200 + 3200x + -1x2 = 3200 + -3200 Combine like terms: 3200 + -3200 = 0 -3200 + 3200x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3200 + -3200x + x2 = 0 Move the constant term to the right: Add '-3200' to each side of the equation. 3200 + -3200x + -3200 + x2 = 0 + -3200 Reorder the terms: 3200 + -3200 + -3200x + x2 = 0 + -3200 Combine like terms: 3200 + -3200 = 0 0 + -3200x + x2 = 0 + -3200 -3200x + x2 = 0 + -3200 Combine like terms: 0 + -3200 = -3200 -3200x + x2 = -3200 The x term is -3200x. Take half its coefficient (-1600). Square it (2560000) and add it to both sides. Add '2560000' to each side of the equation. -3200x + 2560000 + x2 = -3200 + 2560000 Reorder the terms: 2560000 + -3200x + x2 = -3200 + 2560000 Combine like terms: -3200 + 2560000 = 2556800 2560000 + -3200x + x2 = 2556800 Factor a perfect square on the left side: (x + -1600)(x + -1600) = 2556800 Calculate the square root of the right side: 1598.999687305 Break this problem into two subproblems by setting (x + -1600) equal to 1598.999687305 and -1598.999687305.Subproblem 1
x + -1600 = 1598.999687305 Simplifying x + -1600 = 1598.999687305 Reorder the terms: -1600 + x = 1598.999687305 Solving -1600 + x = 1598.999687305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1600' to each side of the equation. -1600 + 1600 + x = 1598.999687305 + 1600 Combine like terms: -1600 + 1600 = 0 0 + x = 1598.999687305 + 1600 x = 1598.999687305 + 1600 Combine like terms: 1598.999687305 + 1600 = 3198.999687305 x = 3198.999687305 Simplifying x = 3198.999687305Subproblem 2
x + -1600 = -1598.999687305 Simplifying x + -1600 = -1598.999687305 Reorder the terms: -1600 + x = -1598.999687305 Solving -1600 + x = -1598.999687305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1600' to each side of the equation. -1600 + 1600 + x = -1598.999687305 + 1600 Combine like terms: -1600 + 1600 = 0 0 + x = -1598.999687305 + 1600 x = -1598.999687305 + 1600 Combine like terms: -1598.999687305 + 1600 = 1.000312695 x = 1.000312695 Simplifying x = 1.000312695Solution
The solution to the problem is based on the solutions from the subproblems. x = {3198.999687305, 1.000312695}
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