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Simplifying (y + -8)(y + -8) + -28 = 0 Reorder the terms: (-8 + y)(y + -8) + -28 = 0 Reorder the terms: (-8 + y)(-8 + y) + -28 = 0 Multiply (-8 + y) * (-8 + y) (-8(-8 + y) + y(-8 + y)) + -28 = 0 ((-8 * -8 + y * -8) + y(-8 + y)) + -28 = 0 ((64 + -8y) + y(-8 + y)) + -28 = 0 (64 + -8y + (-8 * y + y * y)) + -28 = 0 (64 + -8y + (-8y + y2)) + -28 = 0 Combine like terms: -8y + -8y = -16y (64 + -16y + y2) + -28 = 0 Reorder the terms: 64 + -28 + -16y + y2 = 0 Combine like terms: 64 + -28 = 36 36 + -16y + y2 = 0 Solving 36 + -16y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -16y + -36 + y2 = 0 + -36 Reorder the terms: 36 + -36 + -16y + y2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -16y + y2 = 0 + -36 -16y + y2 = 0 + -36 Combine like terms: 0 + -36 = -36 -16y + y2 = -36 The y term is -16y. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16y + 64 + y2 = -36 + 64 Reorder the terms: 64 + -16y + y2 = -36 + 64 Combine like terms: -36 + 64 = 28 64 + -16y + y2 = 28 Factor a perfect square on the left side: (y + -8)(y + -8) = 28 Calculate the square root of the right side: 5.291502622 Break this problem into two subproblems by setting (y + -8) equal to 5.291502622 and -5.291502622.Subproblem 1
y + -8 = 5.291502622 Simplifying y + -8 = 5.291502622 Reorder the terms: -8 + y = 5.291502622 Solving -8 + y = 5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = 5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + y = 5.291502622 + 8 y = 5.291502622 + 8 Combine like terms: 5.291502622 + 8 = 13.291502622 y = 13.291502622 Simplifying y = 13.291502622Subproblem 2
y + -8 = -5.291502622 Simplifying y + -8 = -5.291502622 Reorder the terms: -8 + y = -5.291502622 Solving -8 + y = -5.291502622 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = -5.291502622 + 8 Combine like terms: -8 + 8 = 0 0 + y = -5.291502622 + 8 y = -5.291502622 + 8 Combine like terms: -5.291502622 + 8 = 2.708497378 y = 2.708497378 Simplifying y = 2.708497378Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.291502622, 2.708497378}
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