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Simplifying y2 = 18y + 18 Reorder the terms: y2 = 18 + 18y Solving y2 = 18 + 18y Solving for variable 'y'. Reorder the terms: -18 + -18y + y2 = 18 + 18y + -18 + -18y Reorder the terms: -18 + -18y + y2 = 18 + -18 + 18y + -18y Combine like terms: 18 + -18 = 0 -18 + -18y + y2 = 0 + 18y + -18y -18 + -18y + y2 = 18y + -18y Combine like terms: 18y + -18y = 0 -18 + -18y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -18y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + -18y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -18y + y2 = 0 + 18 -18y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 -18y + y2 = 18 The y term is -18y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y + 81 + y2 = 18 + 81 Reorder the terms: 81 + -18y + y2 = 18 + 81 Combine like terms: 18 + 81 = 99 81 + -18y + y2 = 99 Factor a perfect square on the left side: (y + -9)(y + -9) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (y + -9) equal to 9.949874371 and -9.949874371.Subproblem 1
y + -9 = 9.949874371 Simplifying y + -9 = 9.949874371 Reorder the terms: -9 + y = 9.949874371 Solving -9 + y = 9.949874371 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 9.949874371 + 9 Combine like terms: -9 + 9 = 0 0 + y = 9.949874371 + 9 y = 9.949874371 + 9 Combine like terms: 9.949874371 + 9 = 18.949874371 y = 18.949874371 Simplifying y = 18.949874371Subproblem 2
y + -9 = -9.949874371 Simplifying y + -9 = -9.949874371 Reorder the terms: -9 + y = -9.949874371 Solving -9 + y = -9.949874371 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -9.949874371 + 9 Combine like terms: -9 + 9 = 0 0 + y = -9.949874371 + 9 y = -9.949874371 + 9 Combine like terms: -9.949874371 + 9 = -0.949874371 y = -0.949874371 Simplifying y = -0.949874371Solution
The solution to the problem is based on the solutions from the subproblems. y = {18.949874371, -0.949874371}
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