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Simplifying -2y + 3y2 = 12 Solving -2y + 3y2 = 12 Solving for variable 'y'. Reorder the terms: -12 + -2y + 3y2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -2y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + -0.6666666667y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.6666666667y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -0.6666666667y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.6666666667y + y2 = 0 + 4 -0.6666666667y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.6666666667y + y2 = 4 The y term is -0.6666666667y. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667y + 0.1111111112 + y2 = 4 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667y + y2 = 4 + 0.1111111112 Combine like terms: 4 + 0.1111111112 = 4.1111111112 0.1111111112 + -0.6666666667y + y2 = 4.1111111112 Factor a perfect square on the left side: (y + -0.3333333334)(y + -0.3333333334) = 4.1111111112 Calculate the square root of the right side: 2.02758751 Break this problem into two subproblems by setting (y + -0.3333333334) equal to 2.02758751 and -2.02758751.Subproblem 1
y + -0.3333333334 = 2.02758751 Simplifying y + -0.3333333334 = 2.02758751 Reorder the terms: -0.3333333334 + y = 2.02758751 Solving -0.3333333334 + y = 2.02758751 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + y = 2.02758751 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + y = 2.02758751 + 0.3333333334 y = 2.02758751 + 0.3333333334 Combine like terms: 2.02758751 + 0.3333333334 = 2.3609208434 y = 2.3609208434 Simplifying y = 2.3609208434Subproblem 2
y + -0.3333333334 = -2.02758751 Simplifying y + -0.3333333334 = -2.02758751 Reorder the terms: -0.3333333334 + y = -2.02758751 Solving -0.3333333334 + y = -2.02758751 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + y = -2.02758751 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + y = -2.02758751 + 0.3333333334 y = -2.02758751 + 0.3333333334 Combine like terms: -2.02758751 + 0.3333333334 = -1.6942541766 y = -1.6942541766 Simplifying y = -1.6942541766Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.3609208434, -1.6942541766}
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