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Simplifying y2 + -24y + -9 = 0 Reorder the terms: -9 + -24y + y2 = 0 Solving -9 + -24y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -24y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -24y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -24y + y2 = 0 + 9 -24y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -24y + y2 = 9 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 = 9 + 144 Reorder the terms: 144 + -24y + y2 = 9 + 144 Combine like terms: 9 + 144 = 153 144 + -24y + y2 = 153 Factor a perfect square on the left side: (y + -12)(y + -12) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (y + -12) equal to 12.369316877 and -12.369316877.Subproblem 1
y + -12 = 12.369316877 Simplifying y + -12 = 12.369316877 Reorder the terms: -12 + y = 12.369316877 Solving -12 + y = 12.369316877 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 = 12.369316877 + 12 Combine like terms: -12 + 12 = 0 0 + y = 12.369316877 + 12 y = 12.369316877 + 12 Combine like terms: 12.369316877 + 12 = 24.369316877 y = 24.369316877 Simplifying y = 24.369316877Subproblem 2
y + -12 = -12.369316877 Simplifying y + -12 = -12.369316877 Reorder the terms: -12 + y = -12.369316877 Solving -12 + y = -12.369316877 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 = -12.369316877 + 12 Combine like terms: -12 + 12 = 0 0 + y = -12.369316877 + 12 y = -12.369316877 + 12 Combine like terms: -12.369316877 + 12 = -0.369316877 y = -0.369316877 Simplifying y = -0.369316877Solution
The solution to the problem is based on the solutions from the subproblems. y = {24.369316877, -0.369316877}
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