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Simplifying 470y2 + 34545000 + -263200y = y Reorder the terms: 34545000 + -263200y + 470y2 = y Solving 34545000 + -263200y + 470y2 = y Solving for variable 'y'. Reorder the terms: 34545000 + -263200y + -1y + 470y2 = y + -1y Combine like terms: -263200y + -1y = -263201y 34545000 + -263201y + 470y2 = y + -1y Combine like terms: y + -1y = 0 34545000 + -263201y + 470y2 = 0 Begin completing the square. Divide all terms by 470 the coefficient of the squared term: Divide each side by '470'. 73500 + -560.0021277y + y2 = 0 Move the constant term to the right: Add '-73500' to each side of the equation. 73500 + -560.0021277y + -73500 + y2 = 0 + -73500 Reorder the terms: 73500 + -73500 + -560.0021277y + y2 = 0 + -73500 Combine like terms: 73500 + -73500 = 0 0 + -560.0021277y + y2 = 0 + -73500 -560.0021277y + y2 = 0 + -73500 Combine like terms: 0 + -73500 = -73500 -560.0021277y + y2 = -73500 The y term is -560.0021277y. Take half its coefficient (-280.0010639). Square it (78400.59579) and add it to both sides. Add '78400.59579' to each side of the equation. -560.0021277y + 78400.59579 + y2 = -73500 + 78400.59579 Reorder the terms: 78400.59579 + -560.0021277y + y2 = -73500 + 78400.59579 Combine like terms: -73500 + 78400.59579 = 4900.59579 78400.59579 + -560.0021277y + y2 = 4900.59579 Factor a perfect square on the left side: (y + -280.0010639)(y + -280.0010639) = 4900.59579 Calculate the square root of the right side: 70.004255514 Break this problem into two subproblems by setting (y + -280.0010639) equal to 70.004255514 and -70.004255514.Subproblem 1
y + -280.0010639 = 70.004255514 Simplifying y + -280.0010639 = 70.004255514 Reorder the terms: -280.0010639 + y = 70.004255514 Solving -280.0010639 + y = 70.004255514 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '280.0010639' to each side of the equation. -280.0010639 + 280.0010639 + y = 70.004255514 + 280.0010639 Combine like terms: -280.0010639 + 280.0010639 = 0.0000000 0.0000000 + y = 70.004255514 + 280.0010639 y = 70.004255514 + 280.0010639 Combine like terms: 70.004255514 + 280.0010639 = 350.005319414 y = 350.005319414 Simplifying y = 350.005319414Subproblem 2
y + -280.0010639 = -70.004255514 Simplifying y + -280.0010639 = -70.004255514 Reorder the terms: -280.0010639 + y = -70.004255514 Solving -280.0010639 + y = -70.004255514 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '280.0010639' to each side of the equation. -280.0010639 + 280.0010639 + y = -70.004255514 + 280.0010639 Combine like terms: -280.0010639 + 280.0010639 = 0.0000000 0.0000000 + y = -70.004255514 + 280.0010639 y = -70.004255514 + 280.0010639 Combine like terms: -70.004255514 + 280.0010639 = 209.996808386 y = 209.996808386 Simplifying y = 209.996808386Solution
The solution to the problem is based on the solutions from the subproblems. y = {350.005319414, 209.996808386}
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