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Simplifying (7y + 6)(4y + -9) = 104 Reorder the terms: (6 + 7y)(4y + -9) = 104 Reorder the terms: (6 + 7y)(-9 + 4y) = 104 Multiply (6 + 7y) * (-9 + 4y) (6(-9 + 4y) + 7y * (-9 + 4y)) = 104 ((-9 * 6 + 4y * 6) + 7y * (-9 + 4y)) = 104 ((-54 + 24y) + 7y * (-9 + 4y)) = 104 (-54 + 24y + (-9 * 7y + 4y * 7y)) = 104 (-54 + 24y + (-63y + 28y2)) = 104 Combine like terms: 24y + -63y = -39y (-54 + -39y + 28y2) = 104 Solving -54 + -39y + 28y2 = 104 Solving for variable 'y'. Reorder the terms: -54 + -104 + -39y + 28y2 = 104 + -104 Combine like terms: -54 + -104 = -158 -158 + -39y + 28y2 = 104 + -104 Combine like terms: 104 + -104 = 0 -158 + -39y + 28y2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -5.642857143 + -1.392857143y + y2 = 0 Move the constant term to the right: Add '5.642857143' to each side of the equation. -5.642857143 + -1.392857143y + 5.642857143 + y2 = 0 + 5.642857143 Reorder the terms: -5.642857143 + 5.642857143 + -1.392857143y + y2 = 0 + 5.642857143 Combine like terms: -5.642857143 + 5.642857143 = 0.000000000 0.000000000 + -1.392857143y + y2 = 0 + 5.642857143 -1.392857143y + y2 = 0 + 5.642857143 Combine like terms: 0 + 5.642857143 = 5.642857143 -1.392857143y + y2 = 5.642857143 The y term is -1.392857143y. Take half its coefficient (-0.6964285715). Square it (0.4850127552) and add it to both sides. Add '0.4850127552' to each side of the equation. -1.392857143y + 0.4850127552 + y2 = 5.642857143 + 0.4850127552 Reorder the terms: 0.4850127552 + -1.392857143y + y2 = 5.642857143 + 0.4850127552 Combine like terms: 5.642857143 + 0.4850127552 = 6.1278698982 0.4850127552 + -1.392857143y + y2 = 6.1278698982 Factor a perfect square on the left side: (y + -0.6964285715)(y + -0.6964285715) = 6.1278698982 Calculate the square root of the right side: 2.475453473 Break this problem into two subproblems by setting (y + -0.6964285715) equal to 2.475453473 and -2.475453473.Subproblem 1
y + -0.6964285715 = 2.475453473 Simplifying y + -0.6964285715 = 2.475453473 Reorder the terms: -0.6964285715 + y = 2.475453473 Solving -0.6964285715 + y = 2.475453473 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6964285715' to each side of the equation. -0.6964285715 + 0.6964285715 + y = 2.475453473 + 0.6964285715 Combine like terms: -0.6964285715 + 0.6964285715 = 0.0000000000 0.0000000000 + y = 2.475453473 + 0.6964285715 y = 2.475453473 + 0.6964285715 Combine like terms: 2.475453473 + 0.6964285715 = 3.1718820445 y = 3.1718820445 Simplifying y = 3.1718820445Subproblem 2
y + -0.6964285715 = -2.475453473 Simplifying y + -0.6964285715 = -2.475453473 Reorder the terms: -0.6964285715 + y = -2.475453473 Solving -0.6964285715 + y = -2.475453473 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.6964285715' to each side of the equation. -0.6964285715 + 0.6964285715 + y = -2.475453473 + 0.6964285715 Combine like terms: -0.6964285715 + 0.6964285715 = 0.0000000000 0.0000000000 + y = -2.475453473 + 0.6964285715 y = -2.475453473 + 0.6964285715 Combine like terms: -2.475453473 + 0.6964285715 = -1.7790249015 y = -1.7790249015 Simplifying y = -1.7790249015Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.1718820445, -1.7790249015}
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