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Simplifying 9y2 + -45y + 38 = 0 Reorder the terms: 38 + -45y + 9y2 = 0 Solving 38 + -45y + 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'. 4.222222222 + -5y + y2 = 0 Move the constant term to the right: Add '-4.222222222' to each side of the equation. 4.222222222 + -5y + -4.222222222 + y2 = 0 + -4.222222222 Reorder the terms: 4.222222222 + -4.222222222 + -5y + y2 = 0 + -4.222222222 Combine like terms: 4.222222222 + -4.222222222 = 0.000000000 0.000000000 + -5y + y2 = 0 + -4.222222222 -5y + y2 = 0 + -4.222222222 Combine like terms: 0 + -4.222222222 = -4.222222222 -5y + y2 = -4.222222222 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = -4.222222222 + 6.25 Reorder the terms: 6.25 + -5y + y2 = -4.222222222 + 6.25 Combine like terms: -4.222222222 + 6.25 = 2.027777778 6.25 + -5y + y2 = 2.027777778 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 2.027777778 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (y + -2.5) equal to 1.424000624 and -1.424000624.Subproblem 1
y + -2.5 = 1.424000624 Simplifying y + -2.5 = 1.424000624 Reorder the terms: -2.5 + y = 1.424000624 Solving -2.5 + y = 1.424000624 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 1.424000624 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 1.424000624 + 2.5 y = 1.424000624 + 2.5 Combine like terms: 1.424000624 + 2.5 = 3.924000624 y = 3.924000624 Simplifying y = 3.924000624Subproblem 2
y + -2.5 = -1.424000624 Simplifying y + -2.5 = -1.424000624 Reorder the terms: -2.5 + y = -1.424000624 Solving -2.5 + y = -1.424000624 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -1.424000624 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -1.424000624 + 2.5 y = -1.424000624 + 2.5 Combine like terms: -1.424000624 + 2.5 = 1.075999376 y = 1.075999376 Simplifying y = 1.075999376Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.924000624, 1.075999376}
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