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Simplifying y2 + -24y + -32 = 0 Reorder the terms: -32 + -24y + y2 = 0 Solving -32 + -24y + 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 + -24y + 32 + y2 = 0 + 32 Reorder the terms: -32 + 32 + -24y + y2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -24y + y2 = 0 + 32 -24y + y2 = 0 + 32 Combine like terms: 0 + 32 = 32 -24y + y2 = 32 The y term is -24y. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24y + 144 + y2 = 32 + 144 Reorder the terms: 144 + -24y + y2 = 32 + 144 Combine like terms: 32 + 144 = 176 144 + -24y + y2 = 176 Factor a perfect square on the left side: (y + -12)(y + -12) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (y + -12) equal to 13.266499161 and -13.266499161.Subproblem 1
y + -12 = 13.266499161 Simplifying y + -12 = 13.266499161 Reorder the terms: -12 + y = 13.266499161 Solving -12 + y = 13.266499161 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = 13.266499161 + 12 Combine like terms: -12 + 12 = 0 0 + y = 13.266499161 + 12 y = 13.266499161 + 12 Combine like terms: 13.266499161 + 12 = 25.266499161 y = 25.266499161 Simplifying y = 25.266499161Subproblem 2
y + -12 = -13.266499161 Simplifying y + -12 = -13.266499161 Reorder the terms: -12 + y = -13.266499161 Solving -12 + y = -13.266499161 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = -13.266499161 + 12 Combine like terms: -12 + 12 = 0 0 + y = -13.266499161 + 12 y = -13.266499161 + 12 Combine like terms: -13.266499161 + 12 = -1.266499161 y = -1.266499161 Simplifying y = -1.266499161Solution
The solution to the problem is based on the solutions from the subproblems. y = {25.266499161, -1.266499161}
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