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Simplifying 796.5 = 35.5y + 0.875y2 Solving 796.5 = 35.5y + 0.875y2 Solving for variable 'y'. Reorder the terms: 796.5 + -35.5y + -0.875y2 = 35.5y + -35.5y + 0.875y2 + -0.875y2 Combine like terms: 35.5y + -35.5y = 0.0 796.5 + -35.5y + -0.875y2 = 0.0 + 0.875y2 + -0.875y2 796.5 + -35.5y + -0.875y2 = 0.875y2 + -0.875y2 Combine like terms: 0.875y2 + -0.875y2 = 0.000 796.5 + -35.5y + -0.875y2 = 0.000 Begin completing the square. Divide all terms by -0.875 the coefficient of the squared term: Divide each side by '-0.875'. -910.2857143 + 40.57142857y + y2 = 0 Move the constant term to the right: Add '910.2857143' to each side of the equation. -910.2857143 + 40.57142857y + 910.2857143 + y2 = 0 + 910.2857143 Reorder the terms: -910.2857143 + 910.2857143 + 40.57142857y + y2 = 0 + 910.2857143 Combine like terms: -910.2857143 + 910.2857143 = 0.0000000 0.0000000 + 40.57142857y + y2 = 0 + 910.2857143 40.57142857y + y2 = 0 + 910.2857143 Combine like terms: 0 + 910.2857143 = 910.2857143 40.57142857y + y2 = 910.2857143 The y term is 40.57142857y. Take half its coefficient (20.28571429). Square it (411.5102043) and add it to both sides. Add '411.5102043' to each side of the equation. 40.57142857y + 411.5102043 + y2 = 910.2857143 + 411.5102043 Reorder the terms: 411.5102043 + 40.57142857y + y2 = 910.2857143 + 411.5102043 Combine like terms: 910.2857143 + 411.5102043 = 1321.7959186 411.5102043 + 40.57142857y + y2 = 1321.7959186 Factor a perfect square on the left side: (y + 20.28571429)(y + 20.28571429) = 1321.7959186 Calculate the square root of the right side: 36.356511365 Break this problem into two subproblems by setting (y + 20.28571429) equal to 36.356511365 and -36.356511365.Subproblem 1
y + 20.28571429 = 36.356511365 Simplifying y + 20.28571429 = 36.356511365 Reorder the terms: 20.28571429 + y = 36.356511365 Solving 20.28571429 + y = 36.356511365 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-20.28571429' to each side of the equation. 20.28571429 + -20.28571429 + y = 36.356511365 + -20.28571429 Combine like terms: 20.28571429 + -20.28571429 = 0.00000000 0.00000000 + y = 36.356511365 + -20.28571429 y = 36.356511365 + -20.28571429 Combine like terms: 36.356511365 + -20.28571429 = 16.070797075 y = 16.070797075 Simplifying y = 16.070797075Subproblem 2
y + 20.28571429 = -36.356511365 Simplifying y + 20.28571429 = -36.356511365 Reorder the terms: 20.28571429 + y = -36.356511365 Solving 20.28571429 + y = -36.356511365 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-20.28571429' to each side of the equation. 20.28571429 + -20.28571429 + y = -36.356511365 + -20.28571429 Combine like terms: 20.28571429 + -20.28571429 = 0.00000000 0.00000000 + y = -36.356511365 + -20.28571429 y = -36.356511365 + -20.28571429 Combine like terms: -36.356511365 + -20.28571429 = -56.642225655 y = -56.642225655 Simplifying y = -56.642225655Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.070797075, -56.642225655}
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