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Simplifying (y + 3)(y + -8) = 9 Reorder the terms: (3 + y)(y + -8) = 9 Reorder the terms: (3 + y)(-8 + y) = 9 Multiply (3 + y) * (-8 + y) (3(-8 + y) + y(-8 + y)) = 9 ((-8 * 3 + y * 3) + y(-8 + y)) = 9 ((-24 + 3y) + y(-8 + y)) = 9 (-24 + 3y + (-8 * y + y * y)) = 9 (-24 + 3y + (-8y + y2)) = 9 Combine like terms: 3y + -8y = -5y (-24 + -5y + y2) = 9 Solving -24 + -5y + y2 = 9 Solving for variable 'y'. Reorder the terms: -24 + -9 + -5y + y2 = 9 + -9 Combine like terms: -24 + -9 = -33 -33 + -5y + y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -33 + -5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -5y + 33 + y2 = 0 + 33 Reorder the terms: -33 + 33 + -5y + y2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -5y + y2 = 0 + 33 -5y + y2 = 0 + 33 Combine like terms: 0 + 33 = 33 -5y + y2 = 33 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 = 33 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 33 + 6.25 Combine like terms: 33 + 6.25 = 39.25 6.25 + -5y + y2 = 39.25 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (y + -2.5) equal to 6.264982043 and -6.264982043.Subproblem 1
y + -2.5 = 6.264982043 Simplifying y + -2.5 = 6.264982043 Reorder the terms: -2.5 + y = 6.264982043 Solving -2.5 + y = 6.264982043 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 = 6.264982043 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 6.264982043 + 2.5 y = 6.264982043 + 2.5 Combine like terms: 6.264982043 + 2.5 = 8.764982043 y = 8.764982043 Simplifying y = 8.764982043Subproblem 2
y + -2.5 = -6.264982043 Simplifying y + -2.5 = -6.264982043 Reorder the terms: -2.5 + y = -6.264982043 Solving -2.5 + y = -6.264982043 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 = -6.264982043 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -6.264982043 + 2.5 y = -6.264982043 + 2.5 Combine like terms: -6.264982043 + 2.5 = -3.764982043 y = -3.764982043 Simplifying y = -3.764982043Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.764982043, -3.764982043}
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