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Simplifying 12y2 + -1 = 2y Reorder the terms: -1 + 12y2 = 2y Solving -1 + 12y2 = 2y Solving for variable 'y'. Reorder the terms: -1 + -2y + 12y2 = 2y + -2y Combine like terms: 2y + -2y = 0 -1 + -2y + 12y2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.08333333333 + -0.1666666667y + y2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -0.1666666667y + 0.08333333333 + y2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -0.1666666667y + y2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -0.1666666667y + y2 = 0 + 0.08333333333 -0.1666666667y + y2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -0.1666666667y + y2 = 0.08333333333 The y term is -0.1666666667y. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667y + 0.006944444447 + y2 = 0.08333333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667y + y2 = 0.08333333333 + 0.006944444447 Combine like terms: 0.08333333333 + 0.006944444447 = 0.090277777777 0.006944444447 + -0.1666666667y + y2 = 0.090277777777 Factor a perfect square on the left side: (y + -0.08333333335)(y + -0.08333333335) = 0.090277777777 Calculate the square root of the right side: 0.300462606 Break this problem into two subproblems by setting (y + -0.08333333335) equal to 0.300462606 and -0.300462606.Subproblem 1
y + -0.08333333335 = 0.300462606 Simplifying y + -0.08333333335 = 0.300462606 Reorder the terms: -0.08333333335 + y = 0.300462606 Solving -0.08333333335 + y = 0.300462606 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + y = 0.300462606 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = 0.300462606 + 0.08333333335 y = 0.300462606 + 0.08333333335 Combine like terms: 0.300462606 + 0.08333333335 = 0.38379593935 y = 0.38379593935 Simplifying y = 0.38379593935Subproblem 2
y + -0.08333333335 = -0.300462606 Simplifying y + -0.08333333335 = -0.300462606 Reorder the terms: -0.08333333335 + y = -0.300462606 Solving -0.08333333335 + y = -0.300462606 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + y = -0.300462606 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = -0.300462606 + 0.08333333335 y = -0.300462606 + 0.08333333335 Combine like terms: -0.300462606 + 0.08333333335 = -0.21712927265 y = -0.21712927265 Simplifying y = -0.21712927265Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.38379593935, -0.21712927265}
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