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Simplifying -9y = 1y2 + -14 Reorder the terms: -9y = -14 + 1y2 Solving -9y = -14 + 1y2 Solving for variable 'y'. Reorder the terms: 14 + -9y + -1y2 = -14 + 1y2 + 14 + -1y2 Reorder the terms: 14 + -9y + -1y2 = -14 + 14 + 1y2 + -1y2 Combine like terms: -14 + 14 = 0 14 + -9y + -1y2 = 0 + 1y2 + -1y2 14 + -9y + -1y2 = 1y2 + -1y2 Combine like terms: 1y2 + -1y2 = 0 14 + -9y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + 9y + y2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + 9y + 14 + y2 = 0 + 14 Reorder the terms: -14 + 14 + 9y + y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 9y + y2 = 0 + 14 9y + y2 = 0 + 14 Combine like terms: 0 + 14 = 14 9y + y2 = 14 The y term is 9y. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9y + 20.25 + y2 = 14 + 20.25 Reorder the terms: 20.25 + 9y + y2 = 14 + 20.25 Combine like terms: 14 + 20.25 = 34.25 20.25 + 9y + y2 = 34.25 Factor a perfect square on the left side: (y + 4.5)(y + 4.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (y + 4.5) equal to 5.852349955 and -5.852349955.Subproblem 1
y + 4.5 = 5.852349955 Simplifying y + 4.5 = 5.852349955 Reorder the terms: 4.5 + y = 5.852349955 Solving 4.5 + y = 5.852349955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = 5.852349955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 5.852349955 + -4.5 y = 5.852349955 + -4.5 Combine like terms: 5.852349955 + -4.5 = 1.352349955 y = 1.352349955 Simplifying y = 1.352349955Subproblem 2
y + 4.5 = -5.852349955 Simplifying y + 4.5 = -5.852349955 Reorder the terms: 4.5 + y = -5.852349955 Solving 4.5 + y = -5.852349955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + y = -5.852349955 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -5.852349955 + -4.5 y = -5.852349955 + -4.5 Combine like terms: -5.852349955 + -4.5 = -10.352349955 y = -10.352349955 Simplifying y = -10.352349955Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.352349955, -10.352349955}
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