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Simplifying 3(y + 3)(y + 3) + 11 = 1040 Reorder the terms: 3(3 + y)(y + 3) + 11 = 1040 Reorder the terms: 3(3 + y)(3 + y) + 11 = 1040 Multiply (3 + y) * (3 + y) 3(3(3 + y) + y(3 + y)) + 11 = 1040 3((3 * 3 + y * 3) + y(3 + y)) + 11 = 1040 3((9 + 3y) + y(3 + y)) + 11 = 1040 3(9 + 3y + (3 * y + y * y)) + 11 = 1040 3(9 + 3y + (3y + y2)) + 11 = 1040 Combine like terms: 3y + 3y = 6y 3(9 + 6y + y2) + 11 = 1040 (9 * 3 + 6y * 3 + y2 * 3) + 11 = 1040 (27 + 18y + 3y2) + 11 = 1040 Reorder the terms: 27 + 11 + 18y + 3y2 = 1040 Combine like terms: 27 + 11 = 38 38 + 18y + 3y2 = 1040 Solving 38 + 18y + 3y2 = 1040 Solving for variable 'y'. Reorder the terms: 38 + -1040 + 18y + 3y2 = 1040 + -1040 Combine like terms: 38 + -1040 = -1002 -1002 + 18y + 3y2 = 1040 + -1040 Combine like terms: 1040 + -1040 = 0 -1002 + 18y + 3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-334 + 6y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-334 + 6y + y2)' equal to zero and attempt to solve: Simplifying -334 + 6y + y2 = 0 Solving -334 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '334' to each side of the equation. -334 + 6y + 334 + y2 = 0 + 334 Reorder the terms: -334 + 334 + 6y + y2 = 0 + 334 Combine like terms: -334 + 334 = 0 0 + 6y + y2 = 0 + 334 6y + y2 = 0 + 334 Combine like terms: 0 + 334 = 334 6y + y2 = 334 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 = 334 + 9 Reorder the terms: 9 + 6y + y2 = 334 + 9 Combine like terms: 334 + 9 = 343 9 + 6y + y2 = 343 Factor a perfect square on the left side: (y + 3)(y + 3) = 343 Calculate the square root of the right side: 18.520259177 Break this problem into two subproblems by setting (y + 3) equal to 18.520259177 and -18.520259177.Subproblem 1
y + 3 = 18.520259177 Simplifying y + 3 = 18.520259177 Reorder the terms: 3 + y = 18.520259177 Solving 3 + y = 18.520259177 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 = 18.520259177 + -3 Combine like terms: 3 + -3 = 0 0 + y = 18.520259177 + -3 y = 18.520259177 + -3 Combine like terms: 18.520259177 + -3 = 15.520259177 y = 15.520259177 Simplifying y = 15.520259177Subproblem 2
y + 3 = -18.520259177 Simplifying y + 3 = -18.520259177 Reorder the terms: 3 + y = -18.520259177 Solving 3 + y = -18.520259177 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 = -18.520259177 + -3 Combine like terms: 3 + -3 = 0 0 + y = -18.520259177 + -3 y = -18.520259177 + -3 Combine like terms: -18.520259177 + -3 = -21.520259177 y = -21.520259177 Simplifying y = -21.520259177Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.520259177, -21.520259177}Solution
y = {15.520259177, -21.520259177}
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