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Simplifying (y + -9)(y + 8) = 4y Reorder the terms: (-9 + y)(y + 8) = 4y Reorder the terms: (-9 + y)(8 + y) = 4y Multiply (-9 + y) * (8 + y) (-9(8 + y) + y(8 + y)) = 4y ((8 * -9 + y * -9) + y(8 + y)) = 4y ((-72 + -9y) + y(8 + y)) = 4y (-72 + -9y + (8 * y + y * y)) = 4y (-72 + -9y + (8y + y2)) = 4y Combine like terms: -9y + 8y = -1y (-72 + -1y + y2) = 4y Solving -72 + -1y + y2 = 4y Solving for variable 'y'. Reorder the terms: -72 + -1y + -4y + y2 = 4y + -4y Combine like terms: -1y + -4y = -5y -72 + -5y + y2 = 4y + -4y Combine like terms: 4y + -4y = 0 -72 + -5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -5y + 72 + y2 = 0 + 72 Reorder the terms: -72 + 72 + -5y + y2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -5y + y2 = 0 + 72 -5y + y2 = 0 + 72 Combine like terms: 0 + 72 = 72 -5y + y2 = 72 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 = 72 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 72 + 6.25 Combine like terms: 72 + 6.25 = 78.25 6.25 + -5y + y2 = 78.25 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (y + -2.5) equal to 8.845903006 and -8.845903006.Subproblem 1
y + -2.5 = 8.845903006 Simplifying y + -2.5 = 8.845903006 Reorder the terms: -2.5 + y = 8.845903006 Solving -2.5 + y = 8.845903006 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 = 8.845903006 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 8.845903006 + 2.5 y = 8.845903006 + 2.5 Combine like terms: 8.845903006 + 2.5 = 11.345903006 y = 11.345903006 Simplifying y = 11.345903006Subproblem 2
y + -2.5 = -8.845903006 Simplifying y + -2.5 = -8.845903006 Reorder the terms: -2.5 + y = -8.845903006 Solving -2.5 + y = -8.845903006 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 = -8.845903006 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -8.845903006 + 2.5 y = -8.845903006 + 2.5 Combine like terms: -8.845903006 + 2.5 = -6.345903006 y = -6.345903006 Simplifying y = -6.345903006Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.345903006, -6.345903006}
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