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Simplifying y2 + 36 = 2y2 + -18y + 41 Reorder the terms: 36 + y2 = 2y2 + -18y + 41 Reorder the terms: 36 + y2 = 41 + -18y + 2y2 Solving 36 + y2 = 41 + -18y + 2y2 Solving for variable 'y'. Reorder the terms: 36 + -41 + 18y + y2 + -2y2 = 41 + -18y + 2y2 + -41 + 18y + -2y2 Combine like terms: 36 + -41 = -5 -5 + 18y + y2 + -2y2 = 41 + -18y + 2y2 + -41 + 18y + -2y2 Combine like terms: y2 + -2y2 = -1y2 -5 + 18y + -1y2 = 41 + -18y + 2y2 + -41 + 18y + -2y2 Reorder the terms: -5 + 18y + -1y2 = 41 + -41 + -18y + 18y + 2y2 + -2y2 Combine like terms: 41 + -41 = 0 -5 + 18y + -1y2 = 0 + -18y + 18y + 2y2 + -2y2 -5 + 18y + -1y2 = -18y + 18y + 2y2 + -2y2 Combine like terms: -18y + 18y = 0 -5 + 18y + -1y2 = 0 + 2y2 + -2y2 -5 + 18y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -5 + 18y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -18y + y2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -18y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -18y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -18y + y2 = 0 + -5 -18y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -18y + y2 = -5 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 = -5 + 81 Reorder the terms: 81 + -18y + y2 = -5 + 81 Combine like terms: -5 + 81 = 76 81 + -18y + y2 = 76 Factor a perfect square on the left side: (y + -9)(y + -9) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (y + -9) equal to 8.717797887 and -8.717797887.Subproblem 1
y + -9 = 8.717797887 Simplifying y + -9 = 8.717797887 Reorder the terms: -9 + y = 8.717797887 Solving -9 + y = 8.717797887 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 = 8.717797887 + 9 Combine like terms: -9 + 9 = 0 0 + y = 8.717797887 + 9 y = 8.717797887 + 9 Combine like terms: 8.717797887 + 9 = 17.717797887 y = 17.717797887 Simplifying y = 17.717797887Subproblem 2
y + -9 = -8.717797887 Simplifying y + -9 = -8.717797887 Reorder the terms: -9 + y = -8.717797887 Solving -9 + y = -8.717797887 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 = -8.717797887 + 9 Combine like terms: -9 + 9 = 0 0 + y = -8.717797887 + 9 y = -8.717797887 + 9 Combine like terms: -8.717797887 + 9 = 0.282202113 y = 0.282202113 Simplifying y = 0.282202113Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.717797887, 0.282202113}
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