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Simplifying y(2y + -5) = 3y + 1 Reorder the terms: y(-5 + 2y) = 3y + 1 (-5 * y + 2y * y) = 3y + 1 (-5y + 2y2) = 3y + 1 Reorder the terms: -5y + 2y2 = 1 + 3y Solving -5y + 2y2 = 1 + 3y Solving for variable 'y'. Reorder the terms: -1 + -5y + -3y + 2y2 = 1 + 3y + -1 + -3y Combine like terms: -5y + -3y = -8y -1 + -8y + 2y2 = 1 + 3y + -1 + -3y Reorder the terms: -1 + -8y + 2y2 = 1 + -1 + 3y + -3y Combine like terms: 1 + -1 = 0 -1 + -8y + 2y2 = 0 + 3y + -3y -1 + -8y + 2y2 = 3y + -3y Combine like terms: 3y + -3y = 0 -1 + -8y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -4y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -4y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -4y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -4y + y2 = 0 + 0.5 -4y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -4y + y2 = 0.5 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 0.5 + 4 Reorder the terms: 4 + -4y + y2 = 0.5 + 4 Combine like terms: 0.5 + 4 = 4.5 4 + -4y + y2 = 4.5 Factor a perfect square on the left side: (y + -2)(y + -2) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (y + -2) equal to 2.121320344 and -2.121320344.Subproblem 1
y + -2 = 2.121320344 Simplifying y + -2 = 2.121320344 Reorder the terms: -2 + y = 2.121320344 Solving -2 + y = 2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 2.121320344 + 2 Combine like terms: -2 + 2 = 0 0 + y = 2.121320344 + 2 y = 2.121320344 + 2 Combine like terms: 2.121320344 + 2 = 4.121320344 y = 4.121320344 Simplifying y = 4.121320344Subproblem 2
y + -2 = -2.121320344 Simplifying y + -2 = -2.121320344 Reorder the terms: -2 + y = -2.121320344 Solving -2 + y = -2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -2.121320344 + 2 Combine like terms: -2 + 2 = 0 0 + y = -2.121320344 + 2 y = -2.121320344 + 2 Combine like terms: -2.121320344 + 2 = -0.121320344 y = -0.121320344 Simplifying y = -0.121320344Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.121320344, -0.121320344}
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