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Simplifying 200 = 3x + -0.01x2 Solving 200 = 3x + -0.01x2 Solving for variable 'x'. Reorder the terms: 200 + -3x + 0.01x2 = 3x + -3x + -0.01x2 + 0.01x2 Combine like terms: 3x + -3x = 0 200 + -3x + 0.01x2 = 0 + -0.01x2 + 0.01x2 200 + -3x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 200 + -3x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 20000 + -300x + x2 = 0 Move the constant term to the right: Add '-20000' to each side of the equation. 20000 + -300x + -20000 + x2 = 0 + -20000 Reorder the terms: 20000 + -20000 + -300x + x2 = 0 + -20000 Combine like terms: 20000 + -20000 = 0 0 + -300x + x2 = 0 + -20000 -300x + x2 = 0 + -20000 Combine like terms: 0 + -20000 = -20000 -300x + x2 = -20000 The x term is -300x. Take half its coefficient (-150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. -300x + 22500 + x2 = -20000 + 22500 Reorder the terms: 22500 + -300x + x2 = -20000 + 22500 Combine like terms: -20000 + 22500 = 2500 22500 + -300x + x2 = 2500 Factor a perfect square on the left side: (x + -150)(x + -150) = 2500 Calculate the square root of the right side: 50 Break this problem into two subproblems by setting (x + -150) equal to 50 and -50.Subproblem 1
x + -150 = 50 Simplifying x + -150 = 50 Reorder the terms: -150 + x = 50 Solving -150 + x = 50 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = 50 + 150 Combine like terms: -150 + 150 = 0 0 + x = 50 + 150 x = 50 + 150 Combine like terms: 50 + 150 = 200 x = 200 Simplifying x = 200Subproblem 2
x + -150 = -50 Simplifying x + -150 = -50 Reorder the terms: -150 + x = -50 Solving -150 + x = -50 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 150 + x = -50 + 150 Combine like terms: -150 + 150 = 0 0 + x = -50 + 150 x = -50 + 150 Combine like terms: -50 + 150 = 100 x = 100 Simplifying x = 100Solution
The solution to the problem is based on the solutions from the subproblems. x = {200, 100}
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