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Simplifying (3y + 8)(3y + 8) = 716 Reorder the terms: (8 + 3y)(3y + 8) = 716 Reorder the terms: (8 + 3y)(8 + 3y) = 716 Multiply (8 + 3y) * (8 + 3y) (8(8 + 3y) + 3y * (8 + 3y)) = 716 ((8 * 8 + 3y * 8) + 3y * (8 + 3y)) = 716 ((64 + 24y) + 3y * (8 + 3y)) = 716 (64 + 24y + (8 * 3y + 3y * 3y)) = 716 (64 + 24y + (24y + 9y2)) = 716 Combine like terms: 24y + 24y = 48y (64 + 48y + 9y2) = 716 Solving 64 + 48y + 9y2 = 716 Solving for variable 'y'. Reorder the terms: 64 + -716 + 48y + 9y2 = 716 + -716 Combine like terms: 64 + -716 = -652 -652 + 48y + 9y2 = 716 + -716 Combine like terms: 716 + -716 = 0 -652 + 48y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -72.44444444 + 5.333333333y + y2 = 0 Move the constant term to the right: Add '72.44444444' to each side of the equation. -72.44444444 + 5.333333333y + 72.44444444 + y2 = 0 + 72.44444444 Reorder the terms: -72.44444444 + 72.44444444 + 5.333333333y + y2 = 0 + 72.44444444 Combine like terms: -72.44444444 + 72.44444444 = 0.00000000 0.00000000 + 5.333333333y + y2 = 0 + 72.44444444 5.333333333y + y2 = 0 + 72.44444444 Combine like terms: 0 + 72.44444444 = 72.44444444 5.333333333y + y2 = 72.44444444 The y term is 5.333333333y. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333y + 7.111111113 + y2 = 72.44444444 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333y + y2 = 72.44444444 + 7.111111113 Combine like terms: 72.44444444 + 7.111111113 = 79.555555553 7.111111113 + 5.333333333y + y2 = 79.555555553 Factor a perfect square on the left side: (y + 2.666666667)(y + 2.666666667) = 79.555555553 Calculate the square root of the right side: 8.919392107 Break this problem into two subproblems by setting (y + 2.666666667) equal to 8.919392107 and -8.919392107.Subproblem 1
y + 2.666666667 = 8.919392107 Simplifying y + 2.666666667 = 8.919392107 Reorder the terms: 2.666666667 + y = 8.919392107 Solving 2.666666667 + y = 8.919392107 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + y = 8.919392107 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + y = 8.919392107 + -2.666666667 y = 8.919392107 + -2.666666667 Combine like terms: 8.919392107 + -2.666666667 = 6.25272544 y = 6.25272544 Simplifying y = 6.25272544Subproblem 2
y + 2.666666667 = -8.919392107 Simplifying y + 2.666666667 = -8.919392107 Reorder the terms: 2.666666667 + y = -8.919392107 Solving 2.666666667 + y = -8.919392107 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + y = -8.919392107 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + y = -8.919392107 + -2.666666667 y = -8.919392107 + -2.666666667 Combine like terms: -8.919392107 + -2.666666667 = -11.586058774 y = -11.586058774 Simplifying y = -11.586058774Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.25272544, -11.586058774}
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