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Simplifying y2 + -9y + -32 = 0 Reorder the terms: -32 + -9y + y2 = 0 Solving -32 + -9y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -9y + 32 + y2 = 0 + 32 Reorder the terms: -32 + 32 + -9y + y2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -9y + y2 = 0 + 32 -9y + y2 = 0 + 32 Combine like terms: 0 + 32 = 32 -9y + y2 = 32 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = 32 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 32 + 20.25 Combine like terms: 32 + 20.25 = 52.25 20.25 + -9y + y2 = 52.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (y + -4.5) equal to 7.228416147 and -7.228416147.Subproblem 1
y + -4.5 = 7.228416147 Simplifying y + -4.5 = 7.228416147 Reorder the terms: -4.5 + y = 7.228416147 Solving -4.5 + y = 7.228416147 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 7.228416147 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 7.228416147 + 4.5 y = 7.228416147 + 4.5 Combine like terms: 7.228416147 + 4.5 = 11.728416147 y = 11.728416147 Simplifying y = 11.728416147Subproblem 2
y + -4.5 = -7.228416147 Simplifying y + -4.5 = -7.228416147 Reorder the terms: -4.5 + y = -7.228416147 Solving -4.5 + y = -7.228416147 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -7.228416147 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -7.228416147 + 4.5 y = -7.228416147 + 4.5 Combine like terms: -7.228416147 + 4.5 = -2.728416147 y = -2.728416147 Simplifying y = -2.728416147Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.728416147, -2.728416147}
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