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Simplifying 3y(3y + -1) + -3(2y) = 2 Reorder the terms: 3y(-1 + 3y) + -3(2y) = 2 (-1 * 3y + 3y * 3y) + -3(2y) = 2 (-3y + 9y2) + -3(2y) = 2 Remove parenthesis around (2y) -3y + 9y2 + -3 * 2y = 2 Multiply -3 * 2 -3y + 9y2 + -6y = 2 Reorder the terms: -3y + -6y + 9y2 = 2 Combine like terms: -3y + -6y = -9y -9y + 9y2 = 2 Solving -9y + 9y2 = 2 Solving for variable 'y'. Reorder the terms: -2 + -9y + 9y2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -9y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.2222222222 + -1y + y2 = 0 Move the constant term to the right: Add '0.2222222222' to each side of the equation. -0.2222222222 + -1y + 0.2222222222 + y2 = 0 + 0.2222222222 Reorder the terms: -0.2222222222 + 0.2222222222 + -1y + y2 = 0 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + -1y + y2 = 0 + 0.2222222222 -1y + y2 = 0 + 0.2222222222 Combine like terms: 0 + 0.2222222222 = 0.2222222222 -1y + y2 = 0.2222222222 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 0.2222222222 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 0.2222222222 + 0.25 Combine like terms: 0.2222222222 + 0.25 = 0.4722222222 0.25 + -1y + y2 = 0.4722222222 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 0.4722222222 Calculate the square root of the right side: 0.687184271 Break this problem into two subproblems by setting (y + -0.5) equal to 0.687184271 and -0.687184271.Subproblem 1
y + -0.5 = 0.687184271 Simplifying y + -0.5 = 0.687184271 Reorder the terms: -0.5 + y = 0.687184271 Solving -0.5 + y = 0.687184271 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 0.687184271 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 0.687184271 + 0.5 y = 0.687184271 + 0.5 Combine like terms: 0.687184271 + 0.5 = 1.187184271 y = 1.187184271 Simplifying y = 1.187184271Subproblem 2
y + -0.5 = -0.687184271 Simplifying y + -0.5 = -0.687184271 Reorder the terms: -0.5 + y = -0.687184271 Solving -0.5 + y = -0.687184271 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -0.687184271 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -0.687184271 + 0.5 y = -0.687184271 + 0.5 Combine like terms: -0.687184271 + 0.5 = -0.187184271 y = -0.187184271 Simplifying y = -0.187184271Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.187184271, -0.187184271}
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