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Simplifying 0.15y + 0.08y(y + 4000) = 1240 Reorder the terms: 0.15y + 0.08y(4000 + y) = 1240 0.15y + (4000 * 0.08y + y * 0.08y) = 1240 0.15y + (320y + 0.08y2) = 1240 Combine like terms: 0.15y + 320y = 320.15y 320.15y + 0.08y2 = 1240 Solving 320.15y + 0.08y2 = 1240 Solving for variable 'y'. Reorder the terms: -1240 + 320.15y + 0.08y2 = 1240 + -1240 Combine like terms: 1240 + -1240 = 0 -1240 + 320.15y + 0.08y2 = 0 Begin completing the square. Divide all terms by 0.08 the coefficient of the squared term: Divide each side by '0.08'. -15500 + 4001.875y + y2 = 0 Move the constant term to the right: Add '15500' to each side of the equation. -15500 + 4001.875y + 15500 + y2 = 0 + 15500 Reorder the terms: -15500 + 15500 + 4001.875y + y2 = 0 + 15500 Combine like terms: -15500 + 15500 = 0 0 + 4001.875y + y2 = 0 + 15500 4001.875y + y2 = 0 + 15500 Combine like terms: 0 + 15500 = 15500 4001.875y + y2 = 15500 The y term is 4001.875y. Take half its coefficient (2000.9375). Square it (4003750.879) and add it to both sides. Add '4003750.879' to each side of the equation. 4001.875y + 4003750.879 + y2 = 15500 + 4003750.879 Reorder the terms: 4003750.879 + 4001.875y + y2 = 15500 + 4003750.879 Combine like terms: 15500 + 4003750.879 = 4019250.879 4003750.879 + 4001.875y + y2 = 4019250.879 Factor a perfect square on the left side: (y + 2000.9375)(y + 2000.9375) = 4019250.879 Calculate the square root of the right side: 2004.806943075 Break this problem into two subproblems by setting (y + 2000.9375) equal to 2004.806943075 and -2004.806943075.Subproblem 1
y + 2000.9375 = 2004.806943075 Simplifying y + 2000.9375 = 2004.806943075 Reorder the terms: 2000.9375 + y = 2004.806943075 Solving 2000.9375 + y = 2004.806943075 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2000.9375' to each side of the equation. 2000.9375 + -2000.9375 + y = 2004.806943075 + -2000.9375 Combine like terms: 2000.9375 + -2000.9375 = 0.0000 0.0000 + y = 2004.806943075 + -2000.9375 y = 2004.806943075 + -2000.9375 Combine like terms: 2004.806943075 + -2000.9375 = 3.869443075 y = 3.869443075 Simplifying y = 3.869443075Subproblem 2
y + 2000.9375 = -2004.806943075 Simplifying y + 2000.9375 = -2004.806943075 Reorder the terms: 2000.9375 + y = -2004.806943075 Solving 2000.9375 + y = -2004.806943075 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2000.9375' to each side of the equation. 2000.9375 + -2000.9375 + y = -2004.806943075 + -2000.9375 Combine like terms: 2000.9375 + -2000.9375 = 0.0000 0.0000 + y = -2004.806943075 + -2000.9375 y = -2004.806943075 + -2000.9375 Combine like terms: -2004.806943075 + -2000.9375 = -4005.744443075 y = -4005.744443075 Simplifying y = -4005.744443075Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.869443075, -4005.744443075}
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