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Simplifying 0.05y + 0.03y(y + 50) = 17.5 Reorder the terms: 0.05y + 0.03y(50 + y) = 17.5 0.05y + (50 * 0.03y + y * 0.03y) = 17.5 0.05y + (1.5y + 0.03y2) = 17.5 Combine like terms: 0.05y + 1.5y = 1.55y 1.55y + 0.03y2 = 17.5 Solving 1.55y + 0.03y2 = 17.5 Solving for variable 'y'. Reorder the terms: -17.5 + 1.55y + 0.03y2 = 17.5 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 -17.5 + 1.55y + 0.03y2 = 0.0 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. -583.3333333 + 51.66666667y + y2 = 0 Move the constant term to the right: Add '583.3333333' to each side of the equation. -583.3333333 + 51.66666667y + 583.3333333 + y2 = 0 + 583.3333333 Reorder the terms: -583.3333333 + 583.3333333 + 51.66666667y + y2 = 0 + 583.3333333 Combine like terms: -583.3333333 + 583.3333333 = 0.0000000 0.0000000 + 51.66666667y + y2 = 0 + 583.3333333 51.66666667y + y2 = 0 + 583.3333333 Combine like terms: 0 + 583.3333333 = 583.3333333 51.66666667y + y2 = 583.3333333 The y term is 51.66666667y. Take half its coefficient (25.83333334). Square it (667.3611115) and add it to both sides. Add '667.3611115' to each side of the equation. 51.66666667y + 667.3611115 + y2 = 583.3333333 + 667.3611115 Reorder the terms: 667.3611115 + 51.66666667y + y2 = 583.3333333 + 667.3611115 Combine like terms: 583.3333333 + 667.3611115 = 1250.6944448 667.3611115 + 51.66666667y + y2 = 1250.6944448 Factor a perfect square on the left side: (y + 25.83333334)(y + 25.83333334) = 1250.6944448 Calculate the square root of the right side: 35.365158628 Break this problem into two subproblems by setting (y + 25.83333334) equal to 35.365158628 and -35.365158628.Subproblem 1
y + 25.83333334 = 35.365158628 Simplifying y + 25.83333334 = 35.365158628 Reorder the terms: 25.83333334 + y = 35.365158628 Solving 25.83333334 + y = 35.365158628 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-25.83333334' to each side of the equation. 25.83333334 + -25.83333334 + y = 35.365158628 + -25.83333334 Combine like terms: 25.83333334 + -25.83333334 = 0.00000000 0.00000000 + y = 35.365158628 + -25.83333334 y = 35.365158628 + -25.83333334 Combine like terms: 35.365158628 + -25.83333334 = 9.531825288 y = 9.531825288 Simplifying y = 9.531825288Subproblem 2
y + 25.83333334 = -35.365158628 Simplifying y + 25.83333334 = -35.365158628 Reorder the terms: 25.83333334 + y = -35.365158628 Solving 25.83333334 + y = -35.365158628 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-25.83333334' to each side of the equation. 25.83333334 + -25.83333334 + y = -35.365158628 + -25.83333334 Combine like terms: 25.83333334 + -25.83333334 = 0.00000000 0.00000000 + y = -35.365158628 + -25.83333334 y = -35.365158628 + -25.83333334 Combine like terms: -35.365158628 + -25.83333334 = -61.198491968 y = -61.198491968 Simplifying y = -61.198491968Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.531825288, -61.198491968}
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