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Simplifying 9y2 + -80y + 92 = 0 Reorder the terms: 92 + -80y + 9y2 = 0 Solving 92 + -80y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 10.22222222 + -8.888888889y + y2 = 0 Move the constant term to the right: Add '-10.22222222' to each side of the equation. 10.22222222 + -8.888888889y + -10.22222222 + y2 = 0 + -10.22222222 Reorder the terms: 10.22222222 + -10.22222222 + -8.888888889y + y2 = 0 + -10.22222222 Combine like terms: 10.22222222 + -10.22222222 = 0.00000000 0.00000000 + -8.888888889y + y2 = 0 + -10.22222222 -8.888888889y + y2 = 0 + -10.22222222 Combine like terms: 0 + -10.22222222 = -10.22222222 -8.888888889y + y2 = -10.22222222 The y term is -8.888888889y. Take half its coefficient (-4.444444445). Square it (19.75308642) and add it to both sides. Add '19.75308642' to each side of the equation. -8.888888889y + 19.75308642 + y2 = -10.22222222 + 19.75308642 Reorder the terms: 19.75308642 + -8.888888889y + y2 = -10.22222222 + 19.75308642 Combine like terms: -10.22222222 + 19.75308642 = 9.5308642 19.75308642 + -8.888888889y + y2 = 9.5308642 Factor a perfect square on the left side: (y + -4.444444445)(y + -4.444444445) = 9.5308642 Calculate the square root of the right side: 3.087209776 Break this problem into two subproblems by setting (y + -4.444444445) equal to 3.087209776 and -3.087209776.Subproblem 1
y + -4.444444445 = 3.087209776 Simplifying y + -4.444444445 = 3.087209776 Reorder the terms: -4.444444445 + y = 3.087209776 Solving -4.444444445 + y = 3.087209776 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + y = 3.087209776 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + y = 3.087209776 + 4.444444445 y = 3.087209776 + 4.444444445 Combine like terms: 3.087209776 + 4.444444445 = 7.531654221 y = 7.531654221 Simplifying y = 7.531654221Subproblem 2
y + -4.444444445 = -3.087209776 Simplifying y + -4.444444445 = -3.087209776 Reorder the terms: -4.444444445 + y = -3.087209776 Solving -4.444444445 + y = -3.087209776 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + y = -3.087209776 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + y = -3.087209776 + 4.444444445 y = -3.087209776 + 4.444444445 Combine like terms: -3.087209776 + 4.444444445 = 1.357234669 y = 1.357234669 Simplifying y = 1.357234669Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.531654221, 1.357234669}
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