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Simplifying (y + 1)(y + 4) = 6 Reorder the terms: (1 + y)(y + 4) = 6 Reorder the terms: (1 + y)(4 + y) = 6 Multiply (1 + y) * (4 + y) (1(4 + y) + y(4 + y)) = 6 ((4 * 1 + y * 1) + y(4 + y)) = 6 ((4 + 1y) + y(4 + y)) = 6 (4 + 1y + (4 * y + y * y)) = 6 (4 + 1y + (4y + y2)) = 6 Combine like terms: 1y + 4y = 5y (4 + 5y + y2) = 6 Solving 4 + 5y + y2 = 6 Solving for variable 'y'. Reorder the terms: 4 + -6 + 5y + y2 = 6 + -6 Combine like terms: 4 + -6 = -2 -2 + 5y + y2 = 6 + -6 Combine like terms: 6 + -6 = 0 -2 + 5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 5y + 2 + y2 = 0 + 2 Reorder the terms: -2 + 2 + 5y + y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 5y + y2 = 0 + 2 5y + y2 = 0 + 2 Combine like terms: 0 + 2 = 2 5y + y2 = 2 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 = 2 + 6.25 Reorder the terms: 6.25 + 5y + y2 = 2 + 6.25 Combine like terms: 2 + 6.25 = 8.25 6.25 + 5y + y2 = 8.25 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (y + 2.5) equal to 2.872281323 and -2.872281323.Subproblem 1
y + 2.5 = 2.872281323 Simplifying y + 2.5 = 2.872281323 Reorder the terms: 2.5 + y = 2.872281323 Solving 2.5 + y = 2.872281323 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 = 2.872281323 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 2.872281323 + -2.5 y = 2.872281323 + -2.5 Combine like terms: 2.872281323 + -2.5 = 0.372281323 y = 0.372281323 Simplifying y = 0.372281323Subproblem 2
y + 2.5 = -2.872281323 Simplifying y + 2.5 = -2.872281323 Reorder the terms: 2.5 + y = -2.872281323 Solving 2.5 + y = -2.872281323 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 = -2.872281323 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -2.872281323 + -2.5 y = -2.872281323 + -2.5 Combine like terms: -2.872281323 + -2.5 = -5.372281323 y = -5.372281323 Simplifying y = -5.372281323Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.372281323, -5.372281323}
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