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Simplifying (y) = -4840y2 + 60808 + -6864 y = -4840y2 + 60808 + -6864 Reorder the terms: y = 60808 + -6864 + -4840y2 Combine like terms: 60808 + -6864 = 53944 y = 53944 + -4840y2 Solving y = 53944 + -4840y2 Solving for variable 'y'. Reorder the terms: -53944 + y + 4840y2 = 53944 + -4840y2 + -53944 + 4840y2 Reorder the terms: -53944 + y + 4840y2 = 53944 + -53944 + -4840y2 + 4840y2 Combine like terms: 53944 + -53944 = 0 -53944 + y + 4840y2 = 0 + -4840y2 + 4840y2 -53944 + y + 4840y2 = -4840y2 + 4840y2 Combine like terms: -4840y2 + 4840y2 = 0 -53944 + y + 4840y2 = 0 Begin completing the square. Divide all terms by 4840 the coefficient of the squared term: Divide each side by '4840'. -11.14545455 + 0.0002066115702y + y2 = 0 Move the constant term to the right: Add '11.14545455' to each side of the equation. -11.14545455 + 0.0002066115702y + 11.14545455 + y2 = 0 + 11.14545455 Reorder the terms: -11.14545455 + 11.14545455 + 0.0002066115702y + y2 = 0 + 11.14545455 Combine like terms: -11.14545455 + 11.14545455 = 0.00000000 0.00000000 + 0.0002066115702y + y2 = 0 + 11.14545455 0.0002066115702y + y2 = 0 + 11.14545455 Combine like terms: 0 + 11.14545455 = 11.14545455 0.0002066115702y + y2 = 11.14545455 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.0002066115702y + 0.25 + y2 = 11.14545455 + 0.25 Reorder the terms: 0.25 + 0.0002066115702y + y2 = 11.14545455 + 0.25 Combine like terms: 11.14545455 + 0.25 = 11.39545455 0.25 + 0.0002066115702y + y2 = 11.39545455 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 11.39545455 Calculate the square root of the right side: 3.375715413 Break this problem into two subproblems by setting (y + 0.5) equal to 3.375715413 and -3.375715413.Subproblem 1
y + 0.5 = 3.375715413 Simplifying y + 0.5 = 3.375715413 Reorder the terms: 0.5 + y = 3.375715413 Solving 0.5 + y = 3.375715413 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 3.375715413 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 3.375715413 + -0.5 y = 3.375715413 + -0.5 Combine like terms: 3.375715413 + -0.5 = 2.875715413 y = 2.875715413 Simplifying y = 2.875715413Subproblem 2
y + 0.5 = -3.375715413 Simplifying y + 0.5 = -3.375715413 Reorder the terms: 0.5 + y = -3.375715413 Solving 0.5 + y = -3.375715413 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -3.375715413 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -3.375715413 + -0.5 y = -3.375715413 + -0.5 Combine like terms: -3.375715413 + -0.5 = -3.875715413 y = -3.875715413 Simplifying y = -3.875715413Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.875715413, -3.875715413}
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