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Simplifying 2y2 + -17y + 30 = y2 + -16 Reorder the terms: 30 + -17y + 2y2 = y2 + -16 Reorder the terms: 30 + -17y + 2y2 = -16 + y2 Solving 30 + -17y + 2y2 = -16 + y2 Solving for variable 'y'. Reorder the terms: 30 + 16 + -17y + 2y2 + -1y2 = -16 + y2 + 16 + -1y2 Combine like terms: 30 + 16 = 46 46 + -17y + 2y2 + -1y2 = -16 + y2 + 16 + -1y2 Combine like terms: 2y2 + -1y2 = 1y2 46 + -17y + 1y2 = -16 + y2 + 16 + -1y2 Reorder the terms: 46 + -17y + 1y2 = -16 + 16 + y2 + -1y2 Combine like terms: -16 + 16 = 0 46 + -17y + 1y2 = 0 + y2 + -1y2 46 + -17y + 1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 46 + -17y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + -17y + -46 + y2 = 0 + -46 Reorder the terms: 46 + -46 + -17y + y2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -17y + y2 = 0 + -46 -17y + y2 = 0 + -46 Combine like terms: 0 + -46 = -46 -17y + y2 = -46 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 = -46 + 72.25 Reorder the terms: 72.25 + -17y + y2 = -46 + 72.25 Combine like terms: -46 + 72.25 = 26.25 72.25 + -17y + y2 = 26.25 Factor a perfect square on the left side: (y + -8.5)(y + -8.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (y + -8.5) equal to 5.123475383 and -5.123475383.Subproblem 1
y + -8.5 = 5.123475383 Simplifying y + -8.5 = 5.123475383 Reorder the terms: -8.5 + y = 5.123475383 Solving -8.5 + y = 5.123475383 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 = 5.123475383 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = 5.123475383 + 8.5 y = 5.123475383 + 8.5 Combine like terms: 5.123475383 + 8.5 = 13.623475383 y = 13.623475383 Simplifying y = 13.623475383Subproblem 2
y + -8.5 = -5.123475383 Simplifying y + -8.5 = -5.123475383 Reorder the terms: -8.5 + y = -5.123475383 Solving -8.5 + y = -5.123475383 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 = -5.123475383 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = -5.123475383 + 8.5 y = -5.123475383 + 8.5 Combine like terms: -5.123475383 + 8.5 = 3.376524617 y = 3.376524617 Simplifying y = 3.376524617Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.623475383, 3.376524617}
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