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Simplifying 81 + -18y + y2 = 18 Solving 81 + -18y + y2 = 18 Solving for variable 'y'. Reorder the terms: 81 + -18 + -18y + y2 = 18 + -18 Combine like terms: 81 + -18 = 63 63 + -18y + y2 = 18 + -18 Combine like terms: 18 + -18 = 0 63 + -18y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + -18y + -63 + y2 = 0 + -63 Reorder the terms: 63 + -63 + -18y + y2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + -18y + y2 = 0 + -63 -18y + y2 = 0 + -63 Combine like terms: 0 + -63 = -63 -18y + y2 = -63 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 = -63 + 81 Reorder the terms: 81 + -18y + y2 = -63 + 81 Combine like terms: -63 + 81 = 18 81 + -18y + y2 = 18 Factor a perfect square on the left side: (y + -9)(y + -9) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (y + -9) equal to 4.242640687 and -4.242640687.Subproblem 1
y + -9 = 4.242640687 Simplifying y + -9 = 4.242640687 Reorder the terms: -9 + y = 4.242640687 Solving -9 + y = 4.242640687 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 = 4.242640687 + 9 Combine like terms: -9 + 9 = 0 0 + y = 4.242640687 + 9 y = 4.242640687 + 9 Combine like terms: 4.242640687 + 9 = 13.242640687 y = 13.242640687 Simplifying y = 13.242640687Subproblem 2
y + -9 = -4.242640687 Simplifying y + -9 = -4.242640687 Reorder the terms: -9 + y = -4.242640687 Solving -9 + y = -4.242640687 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 = -4.242640687 + 9 Combine like terms: -9 + 9 = 0 0 + y = -4.242640687 + 9 y = -4.242640687 + 9 Combine like terms: -4.242640687 + 9 = 4.757359313 y = 4.757359313 Simplifying y = 4.757359313Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.242640687, 4.757359313}
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