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Simplifying y2 + -6y + -144 = 0 Reorder the terms: -144 + -6y + y2 = 0 Solving -144 + -6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -6y + 144 + y2 = 0 + 144 Reorder the terms: -144 + 144 + -6y + y2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -6y + y2 = 0 + 144 -6y + y2 = 0 + 144 Combine like terms: 0 + 144 = 144 -6y + y2 = 144 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 144 + 9 Reorder the terms: 9 + -6y + y2 = 144 + 9 Combine like terms: 144 + 9 = 153 9 + -6y + y2 = 153 Factor a perfect square on the left side: (y + -3)(y + -3) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (y + -3) equal to 12.369316877 and -12.369316877.Subproblem 1
y + -3 = 12.369316877 Simplifying y + -3 = 12.369316877 Reorder the terms: -3 + y = 12.369316877 Solving -3 + y = 12.369316877 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 12.369316877 + 3 Combine like terms: -3 + 3 = 0 0 + y = 12.369316877 + 3 y = 12.369316877 + 3 Combine like terms: 12.369316877 + 3 = 15.369316877 y = 15.369316877 Simplifying y = 15.369316877Subproblem 2
y + -3 = -12.369316877 Simplifying y + -3 = -12.369316877 Reorder the terms: -3 + y = -12.369316877 Solving -3 + y = -12.369316877 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -12.369316877 + 3 Combine like terms: -3 + 3 = 0 0 + y = -12.369316877 + 3 y = -12.369316877 + 3 Combine like terms: -12.369316877 + 3 = -9.369316877 y = -9.369316877 Simplifying y = -9.369316877Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.369316877, -9.369316877}
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