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Simplifying 36y2 + -3y + -1 = 0 Reorder the terms: -1 + -3y + 36y2 = 0 Solving -1 + -3y + 36y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.02777777778 + -0.08333333333y + y2 = 0 Move the constant term to the right: Add '0.02777777778' to each side of the equation. -0.02777777778 + -0.08333333333y + 0.02777777778 + y2 = 0 + 0.02777777778 Reorder the terms: -0.02777777778 + 0.02777777778 + -0.08333333333y + y2 = 0 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + -0.08333333333y + y2 = 0 + 0.02777777778 -0.08333333333y + y2 = 0 + 0.02777777778 Combine like terms: 0 + 0.02777777778 = 0.02777777778 -0.08333333333y + y2 = 0.02777777778 The y term is -0.08333333333y. Take half its coefficient (-0.04166666667). Square it (0.001736111111) and add it to both sides. Add '0.001736111111' to each side of the equation. -0.08333333333y + 0.001736111111 + y2 = 0.02777777778 + 0.001736111111 Reorder the terms: 0.001736111111 + -0.08333333333y + y2 = 0.02777777778 + 0.001736111111 Combine like terms: 0.02777777778 + 0.001736111111 = 0.029513888891 0.001736111111 + -0.08333333333y + y2 = 0.029513888891 Factor a perfect square on the left side: (y + -0.04166666667)(y + -0.04166666667) = 0.029513888891 Calculate the square root of the right side: 0.171796068 Break this problem into two subproblems by setting (y + -0.04166666667) equal to 0.171796068 and -0.171796068.Subproblem 1
y + -0.04166666667 = 0.171796068 Simplifying y + -0.04166666667 = 0.171796068 Reorder the terms: -0.04166666667 + y = 0.171796068 Solving -0.04166666667 + y = 0.171796068 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + y = 0.171796068 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + y = 0.171796068 + 0.04166666667 y = 0.171796068 + 0.04166666667 Combine like terms: 0.171796068 + 0.04166666667 = 0.21346273467 y = 0.21346273467 Simplifying y = 0.21346273467Subproblem 2
y + -0.04166666667 = -0.171796068 Simplifying y + -0.04166666667 = -0.171796068 Reorder the terms: -0.04166666667 + y = -0.171796068 Solving -0.04166666667 + y = -0.171796068 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.04166666667' to each side of the equation. -0.04166666667 + 0.04166666667 + y = -0.171796068 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + y = -0.171796068 + 0.04166666667 y = -0.171796068 + 0.04166666667 Combine like terms: -0.171796068 + 0.04166666667 = -0.13012940133 y = -0.13012940133 Simplifying y = -0.13012940133Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.21346273467, -0.13012940133}
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