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Simplifying 0 = -0.02x2 + 190x + -90000 Reorder the terms: 0 = -90000 + 190x + -0.02x2 Solving 0 = -90000 + 190x + -0.02x2 Solving for variable 'x'. Combine like terms: 0 + 90000 = 90000 90000 + -190x + 0.02x2 = -90000 + 190x + -0.02x2 + 90000 + -190x + 0.02x2 Reorder the terms: 90000 + -190x + 0.02x2 = -90000 + 90000 + 190x + -190x + -0.02x2 + 0.02x2 Combine like terms: -90000 + 90000 = 0 90000 + -190x + 0.02x2 = 0 + 190x + -190x + -0.02x2 + 0.02x2 90000 + -190x + 0.02x2 = 190x + -190x + -0.02x2 + 0.02x2 Combine like terms: 190x + -190x = 0 90000 + -190x + 0.02x2 = 0 + -0.02x2 + 0.02x2 90000 + -190x + 0.02x2 = -0.02x2 + 0.02x2 Combine like terms: -0.02x2 + 0.02x2 = 0.00 90000 + -190x + 0.02x2 = 0.00 Begin completing the square. Divide all terms by 0.02 the coefficient of the squared term: Divide each side by '0.02'. 4500000 + -9500x + x2 = 0 Move the constant term to the right: Add '-4500000' to each side of the equation. 4500000 + -9500x + -4500000 + x2 = 0 + -4500000 Reorder the terms: 4500000 + -4500000 + -9500x + x2 = 0 + -4500000 Combine like terms: 4500000 + -4500000 = 0 0 + -9500x + x2 = 0 + -4500000 -9500x + x2 = 0 + -4500000 Combine like terms: 0 + -4500000 = -4500000 -9500x + x2 = -4500000 The x term is -9500x. Take half its coefficient (-4750). Square it (22562500) and add it to both sides. Add '22562500' to each side of the equation. -9500x + 22562500 + x2 = -4500000 + 22562500 Reorder the terms: 22562500 + -9500x + x2 = -4500000 + 22562500 Combine like terms: -4500000 + 22562500 = 18062500 22562500 + -9500x + x2 = 18062500 Factor a perfect square on the left side: (x + -4750)(x + -4750) = 18062500 Calculate the square root of the right side: 4250 Break this problem into two subproblems by setting (x + -4750) equal to 4250 and -4250.Subproblem 1
x + -4750 = 4250 Simplifying x + -4750 = 4250 Reorder the terms: -4750 + x = 4250 Solving -4750 + x = 4250 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4750' to each side of the equation. -4750 + 4750 + x = 4250 + 4750 Combine like terms: -4750 + 4750 = 0 0 + x = 4250 + 4750 x = 4250 + 4750 Combine like terms: 4250 + 4750 = 9000 x = 9000 Simplifying x = 9000Subproblem 2
x + -4750 = -4250 Simplifying x + -4750 = -4250 Reorder the terms: -4750 + x = -4250 Solving -4750 + x = -4250 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4750' to each side of the equation. -4750 + 4750 + x = -4250 + 4750 Combine like terms: -4750 + 4750 = 0 0 + x = -4250 + 4750 x = -4250 + 4750 Combine like terms: -4250 + 4750 = 500 x = 500 Simplifying x = 500Solution
The solution to the problem is based on the solutions from the subproblems. x = {9000, 500}
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