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Simplifying 11y(4 + -6y) + 5(13y + 1) = 9 (4 * 11y + -6y * 11y) + 5(13y + 1) = 9 (44y + -66y2) + 5(13y + 1) = 9 Reorder the terms: 44y + -66y2 + 5(1 + 13y) = 9 44y + -66y2 + (1 * 5 + 13y * 5) = 9 44y + -66y2 + (5 + 65y) = 9 Reorder the terms: 5 + 44y + 65y + -66y2 = 9 Combine like terms: 44y + 65y = 109y 5 + 109y + -66y2 = 9 Solving 5 + 109y + -66y2 = 9 Solving for variable 'y'. Reorder the terms: 5 + -9 + 109y + -66y2 = 9 + -9 Combine like terms: 5 + -9 = -4 -4 + 109y + -66y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -4 + 109y + -66y2 = 0 Begin completing the square. Divide all terms by -66 the coefficient of the squared term: Divide each side by '-66'. 0.06060606061 + -1.651515152y + y2 = 0 Move the constant term to the right: Add '-0.06060606061' to each side of the equation. 0.06060606061 + -1.651515152y + -0.06060606061 + y2 = 0 + -0.06060606061 Reorder the terms: 0.06060606061 + -0.06060606061 + -1.651515152y + y2 = 0 + -0.06060606061 Combine like terms: 0.06060606061 + -0.06060606061 = 0.00000000000 0.00000000000 + -1.651515152y + y2 = 0 + -0.06060606061 -1.651515152y + y2 = 0 + -0.06060606061 Combine like terms: 0 + -0.06060606061 = -0.06060606061 -1.651515152y + y2 = -0.06060606061 The y term is -1.651515152y. Take half its coefficient (-0.825757576). Square it (0.6818755743) and add it to both sides. Add '0.6818755743' to each side of the equation. -1.651515152y + 0.6818755743 + y2 = -0.06060606061 + 0.6818755743 Reorder the terms: 0.6818755743 + -1.651515152y + y2 = -0.06060606061 + 0.6818755743 Combine like terms: -0.06060606061 + 0.6818755743 = 0.62126951369 0.6818755743 + -1.651515152y + y2 = 0.62126951369 Factor a perfect square on the left side: (y + -0.825757576)(y + -0.825757576) = 0.62126951369 Calculate the square root of the right side: 0.788206517 Break this problem into two subproblems by setting (y + -0.825757576) equal to 0.788206517 and -0.788206517.Subproblem 1
y + -0.825757576 = 0.788206517 Simplifying y + -0.825757576 = 0.788206517 Reorder the terms: -0.825757576 + y = 0.788206517 Solving -0.825757576 + y = 0.788206517 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.825757576' to each side of the equation. -0.825757576 + 0.825757576 + y = 0.788206517 + 0.825757576 Combine like terms: -0.825757576 + 0.825757576 = 0.000000000 0.000000000 + y = 0.788206517 + 0.825757576 y = 0.788206517 + 0.825757576 Combine like terms: 0.788206517 + 0.825757576 = 1.613964093 y = 1.613964093 Simplifying y = 1.613964093Subproblem 2
y + -0.825757576 = -0.788206517 Simplifying y + -0.825757576 = -0.788206517 Reorder the terms: -0.825757576 + y = -0.788206517 Solving -0.825757576 + y = -0.788206517 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.825757576' to each side of the equation. -0.825757576 + 0.825757576 + y = -0.788206517 + 0.825757576 Combine like terms: -0.825757576 + 0.825757576 = 0.000000000 0.000000000 + y = -0.788206517 + 0.825757576 y = -0.788206517 + 0.825757576 Combine like terms: -0.788206517 + 0.825757576 = 0.037551059 y = 0.037551059 Simplifying y = 0.037551059Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.613964093, 0.037551059}
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