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Simplifying 18y + y2 = 9 Solving 18y + y2 = 9 Solving for variable 'y'. Reorder the terms: -9 + 18y + y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 18y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 18y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + 18y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 18y + y2 = 0 + 9 18y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 18y + y2 = 9 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 = 9 + 81 Reorder the terms: 81 + 18y + y2 = 9 + 81 Combine like terms: 9 + 81 = 90 81 + 18y + y2 = 90 Factor a perfect square on the left side: (y + 9)(y + 9) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (y + 9) equal to 9.486832981 and -9.486832981.Subproblem 1
y + 9 = 9.486832981 Simplifying y + 9 = 9.486832981 Reorder the terms: 9 + y = 9.486832981 Solving 9 + y = 9.486832981 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 = 9.486832981 + -9 Combine like terms: 9 + -9 = 0 0 + y = 9.486832981 + -9 y = 9.486832981 + -9 Combine like terms: 9.486832981 + -9 = 0.486832981 y = 0.486832981 Simplifying y = 0.486832981Subproblem 2
y + 9 = -9.486832981 Simplifying y + 9 = -9.486832981 Reorder the terms: 9 + y = -9.486832981 Solving 9 + y = -9.486832981 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 = -9.486832981 + -9 Combine like terms: 9 + -9 = 0 0 + y = -9.486832981 + -9 y = -9.486832981 + -9 Combine like terms: -9.486832981 + -9 = -18.486832981 y = -18.486832981 Simplifying y = -18.486832981Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.486832981, -18.486832981}
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