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Simplifying 8(3y + -2) = y(y + 2) + 4 Reorder the terms: 8(-2 + 3y) = y(y + 2) + 4 (-2 * 8 + 3y * 8) = y(y + 2) + 4 (-16 + 24y) = y(y + 2) + 4 Reorder the terms: -16 + 24y = y(2 + y) + 4 -16 + 24y = (2 * y + y * y) + 4 -16 + 24y = (2y + y2) + 4 Reorder the terms: -16 + 24y = 4 + 2y + y2 Solving -16 + 24y = 4 + 2y + y2 Solving for variable 'y'. Reorder the terms: -16 + -4 + 24y + -2y + -1y2 = 4 + 2y + y2 + -4 + -2y + -1y2 Combine like terms: -16 + -4 = -20 -20 + 24y + -2y + -1y2 = 4 + 2y + y2 + -4 + -2y + -1y2 Combine like terms: 24y + -2y = 22y -20 + 22y + -1y2 = 4 + 2y + y2 + -4 + -2y + -1y2 Reorder the terms: -20 + 22y + -1y2 = 4 + -4 + 2y + -2y + y2 + -1y2 Combine like terms: 4 + -4 = 0 -20 + 22y + -1y2 = 0 + 2y + -2y + y2 + -1y2 -20 + 22y + -1y2 = 2y + -2y + y2 + -1y2 Combine like terms: 2y + -2y = 0 -20 + 22y + -1y2 = 0 + y2 + -1y2 -20 + 22y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -20 + 22y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -22y + y2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -22y + -20 + y2 = 0 + -20 Reorder the terms: 20 + -20 + -22y + y2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -22y + y2 = 0 + -20 -22y + y2 = 0 + -20 Combine like terms: 0 + -20 = -20 -22y + y2 = -20 The y term is -22y. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22y + 121 + y2 = -20 + 121 Reorder the terms: 121 + -22y + y2 = -20 + 121 Combine like terms: -20 + 121 = 101 121 + -22y + y2 = 101 Factor a perfect square on the left side: (y + -11)(y + -11) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (y + -11) equal to 10.049875621 and -10.049875621.Subproblem 1
y + -11 = 10.049875621 Simplifying y + -11 = 10.049875621 Reorder the terms: -11 + y = 10.049875621 Solving -11 + y = 10.049875621 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = 10.049875621 + 11 Combine like terms: -11 + 11 = 0 0 + y = 10.049875621 + 11 y = 10.049875621 + 11 Combine like terms: 10.049875621 + 11 = 21.049875621 y = 21.049875621 Simplifying y = 21.049875621Subproblem 2
y + -11 = -10.049875621 Simplifying y + -11 = -10.049875621 Reorder the terms: -11 + y = -10.049875621 Solving -11 + y = -10.049875621 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + y = -10.049875621 + 11 Combine like terms: -11 + 11 = 0 0 + y = -10.049875621 + 11 y = -10.049875621 + 11 Combine like terms: -10.049875621 + 11 = 0.950124379 y = 0.950124379 Simplifying y = 0.950124379Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.049875621, 0.950124379}
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