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Simplifying y2 + -24y + -27 = 0 Reorder the terms: -27 + -24y + y2 = 0 Solving -27 + -24y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -24y + 27 + y2 = 0 + 27 Reorder the terms: -27 + 27 + -24y + y2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -24y + y2 = 0 + 27 -24y + y2 = 0 + 27 Combine like terms: 0 + 27 = 27 -24y + y2 = 27 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 = 27 + 144 Reorder the terms: 144 + -24y + y2 = 27 + 144 Combine like terms: 27 + 144 = 171 144 + -24y + y2 = 171 Factor a perfect square on the left side: (y + -12)(y + -12) = 171 Calculate the square root of the right side: 13.076696831 Break this problem into two subproblems by setting (y + -12) equal to 13.076696831 and -13.076696831.Subproblem 1
y + -12 = 13.076696831 Simplifying y + -12 = 13.076696831 Reorder the terms: -12 + y = 13.076696831 Solving -12 + y = 13.076696831 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 = 13.076696831 + 12 Combine like terms: -12 + 12 = 0 0 + y = 13.076696831 + 12 y = 13.076696831 + 12 Combine like terms: 13.076696831 + 12 = 25.076696831 y = 25.076696831 Simplifying y = 25.076696831Subproblem 2
y + -12 = -13.076696831 Simplifying y + -12 = -13.076696831 Reorder the terms: -12 + y = -13.076696831 Solving -12 + y = -13.076696831 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 = -13.076696831 + 12 Combine like terms: -12 + 12 = 0 0 + y = -13.076696831 + 12 y = -13.076696831 + 12 Combine like terms: -13.076696831 + 12 = -1.076696831 y = -1.076696831 Simplifying y = -1.076696831Solution
The solution to the problem is based on the solutions from the subproblems. y = {25.076696831, -1.076696831}
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