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Simplifying y2 + -24y + 48 = 0 Reorder the terms: 48 + -24y + y2 = 0 Solving 48 + -24y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + -24y + -48 + y2 = 0 + -48 Reorder the terms: 48 + -48 + -24y + y2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -24y + y2 = 0 + -48 -24y + y2 = 0 + -48 Combine like terms: 0 + -48 = -48 -24y + y2 = -48 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 = -48 + 144 Reorder the terms: 144 + -24y + y2 = -48 + 144 Combine like terms: -48 + 144 = 96 144 + -24y + y2 = 96 Factor a perfect square on the left side: (y + -12)(y + -12) = 96 Calculate the square root of the right side: 9.797958971 Break this problem into two subproblems by setting (y + -12) equal to 9.797958971 and -9.797958971.Subproblem 1
y + -12 = 9.797958971 Simplifying y + -12 = 9.797958971 Reorder the terms: -12 + y = 9.797958971 Solving -12 + y = 9.797958971 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 = 9.797958971 + 12 Combine like terms: -12 + 12 = 0 0 + y = 9.797958971 + 12 y = 9.797958971 + 12 Combine like terms: 9.797958971 + 12 = 21.797958971 y = 21.797958971 Simplifying y = 21.797958971Subproblem 2
y + -12 = -9.797958971 Simplifying y + -12 = -9.797958971 Reorder the terms: -12 + y = -9.797958971 Solving -12 + y = -9.797958971 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 = -9.797958971 + 12 Combine like terms: -12 + 12 = 0 0 + y = -9.797958971 + 12 y = -9.797958971 + 12 Combine like terms: -9.797958971 + 12 = 2.202041029 y = 2.202041029 Simplifying y = 2.202041029Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.797958971, 2.202041029}
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