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Simplifying y2 + -18y = 41 Reorder the terms: -18y + y2 = 41 Solving -18y + y2 = 41 Solving for variable 'y'. Reorder the terms: -41 + -18y + y2 = 41 + -41 Combine like terms: 41 + -41 = 0 -41 + -18y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -18y + 41 + y2 = 0 + 41 Reorder the terms: -41 + 41 + -18y + y2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -18y + y2 = 0 + 41 -18y + y2 = 0 + 41 Combine like terms: 0 + 41 = 41 -18y + y2 = 41 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 = 41 + 81 Reorder the terms: 81 + -18y + y2 = 41 + 81 Combine like terms: 41 + 81 = 122 81 + -18y + y2 = 122 Factor a perfect square on the left side: (y + -9)(y + -9) = 122 Calculate the square root of the right side: 11.045361017 Break this problem into two subproblems by setting (y + -9) equal to 11.045361017 and -11.045361017.Subproblem 1
y + -9 = 11.045361017 Simplifying y + -9 = 11.045361017 Reorder the terms: -9 + y = 11.045361017 Solving -9 + y = 11.045361017 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 = 11.045361017 + 9 Combine like terms: -9 + 9 = 0 0 + y = 11.045361017 + 9 y = 11.045361017 + 9 Combine like terms: 11.045361017 + 9 = 20.045361017 y = 20.045361017 Simplifying y = 20.045361017Subproblem 2
y + -9 = -11.045361017 Simplifying y + -9 = -11.045361017 Reorder the terms: -9 + y = -11.045361017 Solving -9 + y = -11.045361017 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 = -11.045361017 + 9 Combine like terms: -9 + 9 = 0 0 + y = -11.045361017 + 9 y = -11.045361017 + 9 Combine like terms: -11.045361017 + 9 = -2.045361017 y = -2.045361017 Simplifying y = -2.045361017Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.045361017, -2.045361017}
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