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Simplifying y2 + -34y + 81 = 0 Reorder the terms: 81 + -34y + y2 = 0 Solving 81 + -34y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-81' to each side of the equation. 81 + -34y + -81 + y2 = 0 + -81 Reorder the terms: 81 + -81 + -34y + y2 = 0 + -81 Combine like terms: 81 + -81 = 0 0 + -34y + y2 = 0 + -81 -34y + y2 = 0 + -81 Combine like terms: 0 + -81 = -81 -34y + y2 = -81 The y term is -34y. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34y + 289 + y2 = -81 + 289 Reorder the terms: 289 + -34y + y2 = -81 + 289 Combine like terms: -81 + 289 = 208 289 + -34y + y2 = 208 Factor a perfect square on the left side: (y + -17)(y + -17) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (y + -17) equal to 14.422205102 and -14.422205102.Subproblem 1
y + -17 = 14.422205102 Simplifying y + -17 = 14.422205102 Reorder the terms: -17 + y = 14.422205102 Solving -17 + y = 14.422205102 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + y = 14.422205102 + 17 Combine like terms: -17 + 17 = 0 0 + y = 14.422205102 + 17 y = 14.422205102 + 17 Combine like terms: 14.422205102 + 17 = 31.422205102 y = 31.422205102 Simplifying y = 31.422205102Subproblem 2
y + -17 = -14.422205102 Simplifying y + -17 = -14.422205102 Reorder the terms: -17 + y = -14.422205102 Solving -17 + y = -14.422205102 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + y = -14.422205102 + 17 Combine like terms: -17 + 17 = 0 0 + y = -14.422205102 + 17 y = -14.422205102 + 17 Combine like terms: -14.422205102 + 17 = 2.577794898 y = 2.577794898 Simplifying y = 2.577794898Solution
The solution to the problem is based on the solutions from the subproblems. y = {31.422205102, 2.577794898}
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