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Simplifying 200x + -1x2 = -20x + 4500 Reorder the terms: 200x + -1x2 = 4500 + -20x Solving 200x + -1x2 = 4500 + -20x Solving for variable 'x'. Reorder the terms: -4500 + 200x + 20x + -1x2 = 4500 + -20x + -4500 + 20x Combine like terms: 200x + 20x = 220x -4500 + 220x + -1x2 = 4500 + -20x + -4500 + 20x Reorder the terms: -4500 + 220x + -1x2 = 4500 + -4500 + -20x + 20x Combine like terms: 4500 + -4500 = 0 -4500 + 220x + -1x2 = 0 + -20x + 20x -4500 + 220x + -1x2 = -20x + 20x Combine like terms: -20x + 20x = 0 -4500 + 220x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4500 + -220x + x2 = 0 Move the constant term to the right: Add '-4500' to each side of the equation. 4500 + -220x + -4500 + x2 = 0 + -4500 Reorder the terms: 4500 + -4500 + -220x + x2 = 0 + -4500 Combine like terms: 4500 + -4500 = 0 0 + -220x + x2 = 0 + -4500 -220x + x2 = 0 + -4500 Combine like terms: 0 + -4500 = -4500 -220x + x2 = -4500 The x term is -220x. Take half its coefficient (-110). Square it (12100) and add it to both sides. Add '12100' to each side of the equation. -220x + 12100 + x2 = -4500 + 12100 Reorder the terms: 12100 + -220x + x2 = -4500 + 12100 Combine like terms: -4500 + 12100 = 7600 12100 + -220x + x2 = 7600 Factor a perfect square on the left side: (x + -110)(x + -110) = 7600 Calculate the square root of the right side: 87.177978871 Break this problem into two subproblems by setting (x + -110) equal to 87.177978871 and -87.177978871.Subproblem 1
x + -110 = 87.177978871 Simplifying x + -110 = 87.177978871 Reorder the terms: -110 + x = 87.177978871 Solving -110 + x = 87.177978871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = 87.177978871 + 110 Combine like terms: -110 + 110 = 0 0 + x = 87.177978871 + 110 x = 87.177978871 + 110 Combine like terms: 87.177978871 + 110 = 197.177978871 x = 197.177978871 Simplifying x = 197.177978871Subproblem 2
x + -110 = -87.177978871 Simplifying x + -110 = -87.177978871 Reorder the terms: -110 + x = -87.177978871 Solving -110 + x = -87.177978871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '110' to each side of the equation. -110 + 110 + x = -87.177978871 + 110 Combine like terms: -110 + 110 = 0 0 + x = -87.177978871 + 110 x = -87.177978871 + 110 Combine like terms: -87.177978871 + 110 = 22.822021129 x = 22.822021129 Simplifying x = 22.822021129Solution
The solution to the problem is based on the solutions from the subproblems. x = {197.177978871, 22.822021129}
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