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Simplifying -0.01x2 + 20x = 4x + 3000 Reorder the terms: 20x + -0.01x2 = 4x + 3000 Reorder the terms: 20x + -0.01x2 = 3000 + 4x Solving 20x + -0.01x2 = 3000 + 4x Solving for variable 'x'. Reorder the terms: -3000 + 20x + -4x + -0.01x2 = 3000 + 4x + -3000 + -4x Combine like terms: 20x + -4x = 16x -3000 + 16x + -0.01x2 = 3000 + 4x + -3000 + -4x Reorder the terms: -3000 + 16x + -0.01x2 = 3000 + -3000 + 4x + -4x Combine like terms: 3000 + -3000 = 0 -3000 + 16x + -0.01x2 = 0 + 4x + -4x -3000 + 16x + -0.01x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -3000 + 16x + -0.01x2 = 0 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 300000 + -1600x + x2 = 0 Move the constant term to the right: Add '-300000' to each side of the equation. 300000 + -1600x + -300000 + x2 = 0 + -300000 Reorder the terms: 300000 + -300000 + -1600x + x2 = 0 + -300000 Combine like terms: 300000 + -300000 = 0 0 + -1600x + x2 = 0 + -300000 -1600x + x2 = 0 + -300000 Combine like terms: 0 + -300000 = -300000 -1600x + x2 = -300000 The x term is -1600x. Take half its coefficient (-800). Square it (640000) and add it to both sides. Add '640000' to each side of the equation. -1600x + 640000 + x2 = -300000 + 640000 Reorder the terms: 640000 + -1600x + x2 = -300000 + 640000 Combine like terms: -300000 + 640000 = 340000 640000 + -1600x + x2 = 340000 Factor a perfect square on the left side: (x + -800)(x + -800) = 340000 Calculate the square root of the right side: 583.095189485 Break this problem into two subproblems by setting (x + -800) equal to 583.095189485 and -583.095189485.Subproblem 1
x + -800 = 583.095189485 Simplifying x + -800 = 583.095189485 Reorder the terms: -800 + x = 583.095189485 Solving -800 + x = 583.095189485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '800' to each side of the equation. -800 + 800 + x = 583.095189485 + 800 Combine like terms: -800 + 800 = 0 0 + x = 583.095189485 + 800 x = 583.095189485 + 800 Combine like terms: 583.095189485 + 800 = 1383.095189485 x = 1383.095189485 Simplifying x = 1383.095189485Subproblem 2
x + -800 = -583.095189485 Simplifying x + -800 = -583.095189485 Reorder the terms: -800 + x = -583.095189485 Solving -800 + x = -583.095189485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '800' to each side of the equation. -800 + 800 + x = -583.095189485 + 800 Combine like terms: -800 + 800 = 0 0 + x = -583.095189485 + 800 x = -583.095189485 + 800 Combine like terms: -583.095189485 + 800 = 216.904810515 x = 216.904810515 Simplifying x = 216.904810515Solution
The solution to the problem is based on the solutions from the subproblems. x = {1383.095189485, 216.904810515}
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