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Simplifying 6y3 + -1y2 + -13y = 0 Reorder the terms: -13y + -1y2 + 6y3 = 0 Solving -13y + -1y2 + 6y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-13 + -1y + 6y2) = 0Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(-13 + -1y + 6y2)' equal to zero and attempt to solve: Simplifying -13 + -1y + 6y2 = 0 Solving -13 + -1y + 6y2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2.166666667 + -0.1666666667y + y2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + -0.1666666667y + 2.166666667 + y2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + -0.1666666667y + y2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + -0.1666666667y + y2 = 0 + 2.166666667 -0.1666666667y + y2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 -0.1666666667y + y2 = 2.166666667 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 = 2.166666667 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667y + y2 = 2.166666667 + 0.006944444447 Combine like terms: 2.166666667 + 0.006944444447 = 2.173611111447 0.006944444447 + -0.1666666667y + y2 = 2.173611111447 Factor a perfect square on the left side: (y + -0.08333333335)(y + -0.08333333335) = 2.173611111447 Calculate the square root of the right side: 1.474317168 Break this problem into two subproblems by setting (y + -0.08333333335) equal to 1.474317168 and -1.474317168.Subproblem 1
y + -0.08333333335 = 1.474317168 Simplifying y + -0.08333333335 = 1.474317168 Reorder the terms: -0.08333333335 + y = 1.474317168 Solving -0.08333333335 + y = 1.474317168 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 = 1.474317168 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = 1.474317168 + 0.08333333335 y = 1.474317168 + 0.08333333335 Combine like terms: 1.474317168 + 0.08333333335 = 1.55765050135 y = 1.55765050135 Simplifying y = 1.55765050135Subproblem 2
y + -0.08333333335 = -1.474317168 Simplifying y + -0.08333333335 = -1.474317168 Reorder the terms: -0.08333333335 + y = -1.474317168 Solving -0.08333333335 + y = -1.474317168 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 = -1.474317168 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + y = -1.474317168 + 0.08333333335 y = -1.474317168 + 0.08333333335 Combine like terms: -1.474317168 + 0.08333333335 = -1.39098383465 y = -1.39098383465 Simplifying y = -1.39098383465Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.55765050135, -1.39098383465}Solution
y = {0, 1.55765050135, -1.39098383465}
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