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Simplifying 3y(y + -8) + 2(y + 7) = 2 Reorder the terms: 3y(-8 + y) + 2(y + 7) = 2 (-8 * 3y + y * 3y) + 2(y + 7) = 2 (-24y + 3y2) + 2(y + 7) = 2 Reorder the terms: -24y + 3y2 + 2(7 + y) = 2 -24y + 3y2 + (7 * 2 + y * 2) = 2 -24y + 3y2 + (14 + 2y) = 2 Reorder the terms: 14 + -24y + 2y + 3y2 = 2 Combine like terms: -24y + 2y = -22y 14 + -22y + 3y2 = 2 Solving 14 + -22y + 3y2 = 2 Solving for variable 'y'. Reorder the terms: 14 + -2 + -22y + 3y2 = 2 + -2 Combine like terms: 14 + -2 = 12 12 + -22y + 3y2 = 2 + -2 Combine like terms: 2 + -2 = 0 12 + -22y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + -7.333333333y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -7.333333333y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -7.333333333y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7.333333333y + y2 = 0 + -4 -7.333333333y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -7.333333333y + y2 = -4 The y term is -7.333333333y. Take half its coefficient (-3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. -7.333333333y + 13.44444445 + y2 = -4 + 13.44444445 Reorder the terms: 13.44444445 + -7.333333333y + y2 = -4 + 13.44444445 Combine like terms: -4 + 13.44444445 = 9.44444445 13.44444445 + -7.333333333y + y2 = 9.44444445 Factor a perfect square on the left side: (y + -3.666666667)(y + -3.666666667) = 9.44444445 Calculate the square root of the right side: 3.073181487 Break this problem into two subproblems by setting (y + -3.666666667) equal to 3.073181487 and -3.073181487.Subproblem 1
y + -3.666666667 = 3.073181487 Simplifying y + -3.666666667 = 3.073181487 Reorder the terms: -3.666666667 + y = 3.073181487 Solving -3.666666667 + y = 3.073181487 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + y = 3.073181487 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + y = 3.073181487 + 3.666666667 y = 3.073181487 + 3.666666667 Combine like terms: 3.073181487 + 3.666666667 = 6.739848154 y = 6.739848154 Simplifying y = 6.739848154Subproblem 2
y + -3.666666667 = -3.073181487 Simplifying y + -3.666666667 = -3.073181487 Reorder the terms: -3.666666667 + y = -3.073181487 Solving -3.666666667 + y = -3.073181487 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.666666667' to each side of the equation. -3.666666667 + 3.666666667 + y = -3.073181487 + 3.666666667 Combine like terms: -3.666666667 + 3.666666667 = 0.000000000 0.000000000 + y = -3.073181487 + 3.666666667 y = -3.073181487 + 3.666666667 Combine like terms: -3.073181487 + 3.666666667 = 0.59348518 y = 0.59348518 Simplifying y = 0.59348518Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.739848154, 0.59348518}
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