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Simplifying 3y2 + 6y + 2 = 48 Reorder the terms: 2 + 6y + 3y2 = 48 Solving 2 + 6y + 3y2 = 48 Solving for variable 'y'. Reorder the terms: 2 + -48 + 6y + 3y2 = 48 + -48 Combine like terms: 2 + -48 = -46 -46 + 6y + 3y2 = 48 + -48 Combine like terms: 48 + -48 = 0 -46 + 6y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -15.33333333 + 2y + y2 = 0 Move the constant term to the right: Add '15.33333333' to each side of the equation. -15.33333333 + 2y + 15.33333333 + y2 = 0 + 15.33333333 Reorder the terms: -15.33333333 + 15.33333333 + 2y + y2 = 0 + 15.33333333 Combine like terms: -15.33333333 + 15.33333333 = 0.00000000 0.00000000 + 2y + y2 = 0 + 15.33333333 2y + y2 = 0 + 15.33333333 Combine like terms: 0 + 15.33333333 = 15.33333333 2y + y2 = 15.33333333 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 15.33333333 + 1 Reorder the terms: 1 + 2y + y2 = 15.33333333 + 1 Combine like terms: 15.33333333 + 1 = 16.33333333 1 + 2y + y2 = 16.33333333 Factor a perfect square on the left side: (y + 1)(y + 1) = 16.33333333 Calculate the square root of the right side: 4.041451884 Break this problem into two subproblems by setting (y + 1) equal to 4.041451884 and -4.041451884.Subproblem 1
y + 1 = 4.041451884 Simplifying y + 1 = 4.041451884 Reorder the terms: 1 + y = 4.041451884 Solving 1 + y = 4.041451884 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 4.041451884 + -1 Combine like terms: 1 + -1 = 0 0 + y = 4.041451884 + -1 y = 4.041451884 + -1 Combine like terms: 4.041451884 + -1 = 3.041451884 y = 3.041451884 Simplifying y = 3.041451884Subproblem 2
y + 1 = -4.041451884 Simplifying y + 1 = -4.041451884 Reorder the terms: 1 + y = -4.041451884 Solving 1 + y = -4.041451884 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -4.041451884 + -1 Combine like terms: 1 + -1 = 0 0 + y = -4.041451884 + -1 y = -4.041451884 + -1 Combine like terms: -4.041451884 + -1 = -5.041451884 y = -5.041451884 Simplifying y = -5.041451884Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.041451884, -5.041451884}
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