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Simplifying 119 + 9y + -1y2 = 0 Solving 119 + 9y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -119 + -9y + y2 = 0 Move the constant term to the right: Add '119' to each side of the equation. -119 + -9y + 119 + y2 = 0 + 119 Reorder the terms: -119 + 119 + -9y + y2 = 0 + 119 Combine like terms: -119 + 119 = 0 0 + -9y + y2 = 0 + 119 -9y + y2 = 0 + 119 Combine like terms: 0 + 119 = 119 -9y + y2 = 119 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 = 119 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 119 + 20.25 Combine like terms: 119 + 20.25 = 139.25 20.25 + -9y + y2 = 139.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 139.25 Calculate the square root of the right side: 11.800423721 Break this problem into two subproblems by setting (y + -4.5) equal to 11.800423721 and -11.800423721.Subproblem 1
y + -4.5 = 11.800423721 Simplifying y + -4.5 = 11.800423721 Reorder the terms: -4.5 + y = 11.800423721 Solving -4.5 + y = 11.800423721 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 = 11.800423721 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 11.800423721 + 4.5 y = 11.800423721 + 4.5 Combine like terms: 11.800423721 + 4.5 = 16.300423721 y = 16.300423721 Simplifying y = 16.300423721Subproblem 2
y + -4.5 = -11.800423721 Simplifying y + -4.5 = -11.800423721 Reorder the terms: -4.5 + y = -11.800423721 Solving -4.5 + y = -11.800423721 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 = -11.800423721 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -11.800423721 + 4.5 y = -11.800423721 + 4.5 Combine like terms: -11.800423721 + 4.5 = -7.300423721 y = -7.300423721 Simplifying y = -7.300423721Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.300423721, -7.300423721}
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