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Simplifying y(y + -2) = 27 Reorder the terms: y(-2 + y) = 27 (-2 * y + y * y) = 27 (-2y + y2) = 27 Solving -2y + y2 = 27 Solving for variable 'y'. Reorder the terms: -27 + -2y + y2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -2y + 27 + y2 = 0 + 27 Reorder the terms: -27 + 27 + -2y + y2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -2y + y2 = 0 + 27 -2y + y2 = 0 + 27 Combine like terms: 0 + 27 = 27 -2y + y2 = 27 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 27 + 1 Reorder the terms: 1 + -2y + y2 = 27 + 1 Combine like terms: 27 + 1 = 28 1 + -2y + y2 = 28 Factor a perfect square on the left side: (y + -1)(y + -1) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (y + -1) equal to 5.291502622 and -5.291502622.Subproblem 1
y + -1 = 5.291502622 Simplifying y + -1 = 5.291502622 Reorder the terms: -1 + y = 5.291502622 Solving -1 + y = 5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + y = 5.291502622 + 1 y = 5.291502622 + 1 Combine like terms: 5.291502622 + 1 = 6.291502622 y = 6.291502622 Simplifying y = 6.291502622Subproblem 2
y + -1 = -5.291502622 Simplifying y + -1 = -5.291502622 Reorder the terms: -1 + y = -5.291502622 Solving -1 + y = -5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -5.291502622 + 1 Combine like terms: -1 + 1 = 0 0 + y = -5.291502622 + 1 y = -5.291502622 + 1 Combine like terms: -5.291502622 + 1 = -4.291502622 y = -4.291502622 Simplifying y = -4.291502622Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.291502622, -4.291502622}
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