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Simplifying 20y = y2 + 2y + 1 Reorder the terms: 20y = 1 + 2y + y2 Solving 20y = 1 + 2y + y2 Solving for variable 'y'. Reorder the terms: -1 + 20y + -2y + -1y2 = 1 + 2y + y2 + -1 + -2y + -1y2 Combine like terms: 20y + -2y = 18y -1 + 18y + -1y2 = 1 + 2y + y2 + -1 + -2y + -1y2 Reorder the terms: -1 + 18y + -1y2 = 1 + -1 + 2y + -2y + y2 + -1y2 Combine like terms: 1 + -1 = 0 -1 + 18y + -1y2 = 0 + 2y + -2y + y2 + -1y2 -1 + 18y + -1y2 = 2y + -2y + y2 + -1y2 Combine like terms: 2y + -2y = 0 -1 + 18y + -1y2 = 0 + y2 + -1y2 -1 + 18y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -1 + 18y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -18y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -18y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -18y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -18y + y2 = 0 + -1 -18y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -18y + y2 = -1 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 = -1 + 81 Reorder the terms: 81 + -18y + y2 = -1 + 81 Combine like terms: -1 + 81 = 80 81 + -18y + y2 = 80 Factor a perfect square on the left side: (y + -9)(y + -9) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (y + -9) equal to 8.94427191 and -8.94427191.Subproblem 1
y + -9 = 8.94427191 Simplifying y + -9 = 8.94427191 Reorder the terms: -9 + y = 8.94427191 Solving -9 + y = 8.94427191 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 = 8.94427191 + 9 Combine like terms: -9 + 9 = 0 0 + y = 8.94427191 + 9 y = 8.94427191 + 9 Combine like terms: 8.94427191 + 9 = 17.94427191 y = 17.94427191 Simplifying y = 17.94427191Subproblem 2
y + -9 = -8.94427191 Simplifying y + -9 = -8.94427191 Reorder the terms: -9 + y = -8.94427191 Solving -9 + y = -8.94427191 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 = -8.94427191 + 9 Combine like terms: -9 + 9 = 0 0 + y = -8.94427191 + 9 y = -8.94427191 + 9 Combine like terms: -8.94427191 + 9 = 0.05572809 y = 0.05572809 Simplifying y = 0.05572809Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.94427191, 0.05572809}
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