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Simplifying y = y2 + -9y + 8 Reorder the terms: y = 8 + -9y + y2 Solving y = 8 + -9y + y2 Solving for variable 'y'. Reorder the terms: -8 + y + 9y + -1y2 = 8 + -9y + y2 + -8 + 9y + -1y2 Combine like terms: y + 9y = 10y -8 + 10y + -1y2 = 8 + -9y + y2 + -8 + 9y + -1y2 Reorder the terms: -8 + 10y + -1y2 = 8 + -8 + -9y + 9y + y2 + -1y2 Combine like terms: 8 + -8 = 0 -8 + 10y + -1y2 = 0 + -9y + 9y + y2 + -1y2 -8 + 10y + -1y2 = -9y + 9y + y2 + -1y2 Combine like terms: -9y + 9y = 0 -8 + 10y + -1y2 = 0 + y2 + -1y2 -8 + 10y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -8 + 10y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -10y + y2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -10y + -8 + y2 = 0 + -8 Reorder the terms: 8 + -8 + -10y + y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -10y + y2 = 0 + -8 -10y + y2 = 0 + -8 Combine like terms: 0 + -8 = -8 -10y + y2 = -8 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = -8 + 25 Reorder the terms: 25 + -10y + y2 = -8 + 25 Combine like terms: -8 + 25 = 17 25 + -10y + y2 = 17 Factor a perfect square on the left side: (y + -5)(y + -5) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (y + -5) equal to 4.123105626 and -4.123105626.Subproblem 1
y + -5 = 4.123105626 Simplifying y + -5 = 4.123105626 Reorder the terms: -5 + y = 4.123105626 Solving -5 + y = 4.123105626 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.123105626 + 5 y = 4.123105626 + 5 Combine like terms: 4.123105626 + 5 = 9.123105626 y = 9.123105626 Simplifying y = 9.123105626Subproblem 2
y + -5 = -4.123105626 Simplifying y + -5 = -4.123105626 Reorder the terms: -5 + y = -4.123105626 Solving -5 + y = -4.123105626 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -4.123105626 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.123105626 + 5 y = -4.123105626 + 5 Combine like terms: -4.123105626 + 5 = 0.876894374 y = 0.876894374 Simplifying y = 0.876894374Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.123105626, 0.876894374}
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