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Simplifying 6y2 + -1y + -9 = 0 Reorder the terms: -9 + -1y + 6y2 = 0 Solving -9 + -1y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + -0.1666666667y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -0.1666666667y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -0.1666666667y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -0.1666666667y + y2 = 0 + 1.5 -0.1666666667y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -0.1666666667y + y2 = 1.5 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 = 1.5 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667y + y2 = 1.5 + 0.006944444447 Combine like terms: 1.5 + 0.006944444447 = 1.506944444447 0.006944444447 + -0.1666666667y + y2 = 1.506944444447 Factor a perfect square on the left side: (y + -0.08333333335)(y + -0.08333333335) = 1.506944444447 Calculate the square root of the right side: 1.227576655 Break this problem into two subproblems by setting (y + -0.08333333335) equal to 1.227576655 and -1.227576655.Subproblem 1
y + -0.08333333335 = 1.227576655 Simplifying y + -0.08333333335 = 1.227576655 Reorder the terms: -0.08333333335 + y = 1.227576655 Solving -0.08333333335 + y = 1.227576655 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 = 1.227576655 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = 1.227576655 + 0.08333333335 y = 1.227576655 + 0.08333333335 Combine like terms: 1.227576655 + 0.08333333335 = 1.31090998835 y = 1.31090998835 Simplifying y = 1.31090998835Subproblem 2
y + -0.08333333335 = -1.227576655 Simplifying y + -0.08333333335 = -1.227576655 Reorder the terms: -0.08333333335 + y = -1.227576655 Solving -0.08333333335 + y = -1.227576655 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 = -1.227576655 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = -1.227576655 + 0.08333333335 y = -1.227576655 + 0.08333333335 Combine like terms: -1.227576655 + 0.08333333335 = -1.14424332165 y = -1.14424332165 Simplifying y = -1.14424332165Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.31090998835, -1.14424332165}
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