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Simplifying 9y2 + -29y + 18 = 0 Reorder the terms: 18 + -29y + 9y2 = 0 Solving 18 + -29y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 2 + -3.222222222y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.222222222y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -3.222222222y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.222222222y + y2 = 0 + -2 -3.222222222y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.222222222y + y2 = -2 The y term is -3.222222222y. Take half its coefficient (-1.611111111). Square it (2.595679012) and add it to both sides. Add '2.595679012' to each side of the equation. -3.222222222y + 2.595679012 + y2 = -2 + 2.595679012 Reorder the terms: 2.595679012 + -3.222222222y + y2 = -2 + 2.595679012 Combine like terms: -2 + 2.595679012 = 0.595679012 2.595679012 + -3.222222222y + y2 = 0.595679012 Factor a perfect square on the left side: (y + -1.611111111)(y + -1.611111111) = 0.595679012 Calculate the square root of the right side: 0.771802444 Break this problem into two subproblems by setting (y + -1.611111111) equal to 0.771802444 and -0.771802444.Subproblem 1
y + -1.611111111 = 0.771802444 Simplifying y + -1.611111111 = 0.771802444 Reorder the terms: -1.611111111 + y = 0.771802444 Solving -1.611111111 + y = 0.771802444 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.611111111' to each side of the equation. -1.611111111 + 1.611111111 + y = 0.771802444 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + y = 0.771802444 + 1.611111111 y = 0.771802444 + 1.611111111 Combine like terms: 0.771802444 + 1.611111111 = 2.382913555 y = 2.382913555 Simplifying y = 2.382913555Subproblem 2
y + -1.611111111 = -0.771802444 Simplifying y + -1.611111111 = -0.771802444 Reorder the terms: -1.611111111 + y = -0.771802444 Solving -1.611111111 + y = -0.771802444 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.611111111' to each side of the equation. -1.611111111 + 1.611111111 + y = -0.771802444 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + y = -0.771802444 + 1.611111111 y = -0.771802444 + 1.611111111 Combine like terms: -0.771802444 + 1.611111111 = 0.839308667 y = 0.839308667 Simplifying y = 0.839308667Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.382913555, 0.839308667}
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