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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 = 4.595679012 2.595679012 + -3.222222222y + y2 = 4.595679012 Factor a perfect square on the left side: (y + -1.611111111)(y + -1.611111111) = 4.595679012 Calculate the square root of the right side: 2.143753487 Break this problem into two subproblems by setting (y + -1.611111111) equal to 2.143753487 and -2.143753487.Subproblem 1
y + -1.611111111 = 2.143753487 Simplifying y + -1.611111111 = 2.143753487 Reorder the terms: -1.611111111 + y = 2.143753487 Solving -1.611111111 + y = 2.143753487 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 = 2.143753487 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + y = 2.143753487 + 1.611111111 y = 2.143753487 + 1.611111111 Combine like terms: 2.143753487 + 1.611111111 = 3.754864598 y = 3.754864598 Simplifying y = 3.754864598Subproblem 2
y + -1.611111111 = -2.143753487 Simplifying y + -1.611111111 = -2.143753487 Reorder the terms: -1.611111111 + y = -2.143753487 Solving -1.611111111 + y = -2.143753487 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 = -2.143753487 + 1.611111111 Combine like terms: -1.611111111 + 1.611111111 = 0.000000000 0.000000000 + y = -2.143753487 + 1.611111111 y = -2.143753487 + 1.611111111 Combine like terms: -2.143753487 + 1.611111111 = -0.532642376 y = -0.532642376 Simplifying y = -0.532642376Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.754864598, -0.532642376}
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