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Simplifying 2y2 + 12y + 3 = 0 Reorder the terms: 3 + 12y + 2y2 = 0 Solving 3 + 12y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 6y + y2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 6y + -1.5 + y2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 6y + y2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 6y + y2 = 0 + -1.5 6y + y2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 6y + y2 = -1.5 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = -1.5 + 9 Reorder the terms: 9 + 6y + y2 = -1.5 + 9 Combine like terms: -1.5 + 9 = 7.5 9 + 6y + y2 = 7.5 Factor a perfect square on the left side: (y + 3)(y + 3) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (y + 3) equal to 2.738612788 and -2.738612788.Subproblem 1
y + 3 = 2.738612788 Simplifying y + 3 = 2.738612788 Reorder the terms: 3 + y = 2.738612788 Solving 3 + y = 2.738612788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 2.738612788 + -3 Combine like terms: 3 + -3 = 0 0 + y = 2.738612788 + -3 y = 2.738612788 + -3 Combine like terms: 2.738612788 + -3 = -0.261387212 y = -0.261387212 Simplifying y = -0.261387212Subproblem 2
y + 3 = -2.738612788 Simplifying y + 3 = -2.738612788 Reorder the terms: 3 + y = -2.738612788 Solving 3 + y = -2.738612788 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -2.738612788 + -3 Combine like terms: 3 + -3 = 0 0 + y = -2.738612788 + -3 y = -2.738612788 + -3 Combine like terms: -2.738612788 + -3 = -5.738612788 y = -5.738612788 Simplifying y = -5.738612788Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.261387212, -5.738612788}
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