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Simplifying -12y2 + 121y + 1 = 0 Reorder the terms: 1 + 121y + -12y2 = 0 Solving 1 + 121y + -12y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.08333333333 + -10.08333333y + y2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -10.08333333y + 0.08333333333 + y2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -10.08333333y + y2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -10.08333333y + y2 = 0 + 0.08333333333 -10.08333333y + y2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -10.08333333y + y2 = 0.08333333333 The y term is -10.08333333y. Take half its coefficient (-5.041666665). Square it (25.41840276) and add it to both sides. Add '25.41840276' to each side of the equation. -10.08333333y + 25.41840276 + y2 = 0.08333333333 + 25.41840276 Reorder the terms: 25.41840276 + -10.08333333y + y2 = 0.08333333333 + 25.41840276 Combine like terms: 0.08333333333 + 25.41840276 = 25.50173609333 25.41840276 + -10.08333333y + y2 = 25.50173609333 Factor a perfect square on the left side: (y + -5.041666665)(y + -5.041666665) = 25.50173609333 Calculate the square root of the right side: 5.049924365 Break this problem into two subproblems by setting (y + -5.041666665) equal to 5.049924365 and -5.049924365.Subproblem 1
y + -5.041666665 = 5.049924365 Simplifying y + -5.041666665 = 5.049924365 Reorder the terms: -5.041666665 + y = 5.049924365 Solving -5.041666665 + y = 5.049924365 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.041666665' to each side of the equation. -5.041666665 + 5.041666665 + y = 5.049924365 + 5.041666665 Combine like terms: -5.041666665 + 5.041666665 = 0.000000000 0.000000000 + y = 5.049924365 + 5.041666665 y = 5.049924365 + 5.041666665 Combine like terms: 5.049924365 + 5.041666665 = 10.09159103 y = 10.09159103 Simplifying y = 10.09159103Subproblem 2
y + -5.041666665 = -5.049924365 Simplifying y + -5.041666665 = -5.049924365 Reorder the terms: -5.041666665 + y = -5.049924365 Solving -5.041666665 + y = -5.049924365 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5.041666665' to each side of the equation. -5.041666665 + 5.041666665 + y = -5.049924365 + 5.041666665 Combine like terms: -5.041666665 + 5.041666665 = 0.000000000 0.000000000 + y = -5.049924365 + 5.041666665 y = -5.049924365 + 5.041666665 Combine like terms: -5.049924365 + 5.041666665 = -0.0082577 y = -0.0082577 Simplifying y = -0.0082577Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.09159103, -0.0082577}
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