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Simplifying 9y2 + 22y + -4 = 0 Reorder the terms: -4 + 22y + 9y2 = 0 Solving -4 + 22y + 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'. -0.4444444444 + 2.444444444y + y2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 2.444444444y + 0.4444444444 + y2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 2.444444444y + y2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 2.444444444y + y2 = 0 + 0.4444444444 2.444444444y + y2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 2.444444444y + y2 = 0.4444444444 The y term is 2.444444444y. Take half its coefficient (1.222222222). Square it (1.493827160) and add it to both sides. Add '1.493827160' to each side of the equation. 2.444444444y + 1.493827160 + y2 = 0.4444444444 + 1.493827160 Reorder the terms: 1.493827160 + 2.444444444y + y2 = 0.4444444444 + 1.493827160 Combine like terms: 0.4444444444 + 1.493827160 = 1.9382716044 1.493827160 + 2.444444444y + y2 = 1.9382716044 Factor a perfect square on the left side: (y + 1.222222222)(y + 1.222222222) = 1.9382716044 Calculate the square root of the right side: 1.392218232 Break this problem into two subproblems by setting (y + 1.222222222) equal to 1.392218232 and -1.392218232.Subproblem 1
y + 1.222222222 = 1.392218232 Simplifying y + 1.222222222 = 1.392218232 Reorder the terms: 1.222222222 + y = 1.392218232 Solving 1.222222222 + y = 1.392218232 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.222222222' to each side of the equation. 1.222222222 + -1.222222222 + y = 1.392218232 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + y = 1.392218232 + -1.222222222 y = 1.392218232 + -1.222222222 Combine like terms: 1.392218232 + -1.222222222 = 0.16999601 y = 0.16999601 Simplifying y = 0.16999601Subproblem 2
y + 1.222222222 = -1.392218232 Simplifying y + 1.222222222 = -1.392218232 Reorder the terms: 1.222222222 + y = -1.392218232 Solving 1.222222222 + y = -1.392218232 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.222222222' to each side of the equation. 1.222222222 + -1.222222222 + y = -1.392218232 + -1.222222222 Combine like terms: 1.222222222 + -1.222222222 = 0.000000000 0.000000000 + y = -1.392218232 + -1.222222222 y = -1.392218232 + -1.222222222 Combine like terms: -1.392218232 + -1.222222222 = -2.614440454 y = -2.614440454 Simplifying y = -2.614440454Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.16999601, -2.614440454}
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