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Simplifying 3y2 + -13y + -6 = 0 Reorder the terms: -6 + -13y + 3y2 = 0 Solving -6 + -13y + 3y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -4.333333333y + y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4.333333333y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + -4.333333333y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4.333333333y + y2 = 0 + 2 -4.333333333y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4.333333333y + y2 = 2 The y term is -4.333333333y. Take half its coefficient (-2.166666667). Square it (4.694444446) and add it to both sides. Add '4.694444446' to each side of the equation. -4.333333333y + 4.694444446 + y2 = 2 + 4.694444446 Reorder the terms: 4.694444446 + -4.333333333y + y2 = 2 + 4.694444446 Combine like terms: 2 + 4.694444446 = 6.694444446 4.694444446 + -4.333333333y + y2 = 6.694444446 Factor a perfect square on the left side: (y + -2.166666667)(y + -2.166666667) = 6.694444446 Calculate the square root of the right side: 2.58736245 Break this problem into two subproblems by setting (y + -2.166666667) equal to 2.58736245 and -2.58736245.Subproblem 1
y + -2.166666667 = 2.58736245 Simplifying y + -2.166666667 = 2.58736245 Reorder the terms: -2.166666667 + y = 2.58736245 Solving -2.166666667 + y = 2.58736245 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + y = 2.58736245 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + y = 2.58736245 + 2.166666667 y = 2.58736245 + 2.166666667 Combine like terms: 2.58736245 + 2.166666667 = 4.754029117 y = 4.754029117 Simplifying y = 4.754029117Subproblem 2
y + -2.166666667 = -2.58736245 Simplifying y + -2.166666667 = -2.58736245 Reorder the terms: -2.166666667 + y = -2.58736245 Solving -2.166666667 + y = -2.58736245 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + y = -2.58736245 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + y = -2.58736245 + 2.166666667 y = -2.58736245 + 2.166666667 Combine like terms: -2.58736245 + 2.166666667 = -0.420695783 y = -0.420695783 Simplifying y = -0.420695783Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.754029117, -0.420695783}
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