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Simplifying (17 + 1y) * y = 17 Reorder the terms for easier multiplication: y(17 + 1y) = 17 (17 * y + 1y * y) = 17 (17y + 1y2) = 17 Solving 17y + 1y2 = 17 Solving for variable 'y'. Reorder the terms: -17 + 17y + 1y2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + 17y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 17y + 17 + y2 = 0 + 17 Reorder the terms: -17 + 17 + 17y + y2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 17y + y2 = 0 + 17 17y + y2 = 0 + 17 Combine like terms: 0 + 17 = 17 17y + y2 = 17 The y term is 17y. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17y + 72.25 + y2 = 17 + 72.25 Reorder the terms: 72.25 + 17y + y2 = 17 + 72.25 Combine like terms: 17 + 72.25 = 89.25 72.25 + 17y + y2 = 89.25 Factor a perfect square on the left side: (y + 8.5)(y + 8.5) = 89.25 Calculate the square root of the right side: 9.447221814 Break this problem into two subproblems by setting (y + 8.5) equal to 9.447221814 and -9.447221814.Subproblem 1
y + 8.5 = 9.447221814 Simplifying y + 8.5 = 9.447221814 Reorder the terms: 8.5 + y = 9.447221814 Solving 8.5 + y = 9.447221814 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + y = 9.447221814 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = 9.447221814 + -8.5 y = 9.447221814 + -8.5 Combine like terms: 9.447221814 + -8.5 = 0.947221814 y = 0.947221814 Simplifying y = 0.947221814Subproblem 2
y + 8.5 = -9.447221814 Simplifying y + 8.5 = -9.447221814 Reorder the terms: 8.5 + y = -9.447221814 Solving 8.5 + y = -9.447221814 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + y = -9.447221814 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = -9.447221814 + -8.5 y = -9.447221814 + -8.5 Combine like terms: -9.447221814 + -8.5 = -17.947221814 y = -17.947221814 Simplifying y = -17.947221814Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.947221814, -17.947221814}
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