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Simplifying y2 + -25y + 54 = 0 Reorder the terms: 54 + -25y + y2 = 0 Solving 54 + -25y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + -25y + -54 + y2 = 0 + -54 Reorder the terms: 54 + -54 + -25y + y2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -25y + y2 = 0 + -54 -25y + y2 = 0 + -54 Combine like terms: 0 + -54 = -54 -25y + y2 = -54 The y term is -25y. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25y + 156.25 + y2 = -54 + 156.25 Reorder the terms: 156.25 + -25y + y2 = -54 + 156.25 Combine like terms: -54 + 156.25 = 102.25 156.25 + -25y + y2 = 102.25 Factor a perfect square on the left side: (y + -12.5)(y + -12.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (y + -12.5) equal to 10.111874208 and -10.111874208.Subproblem 1
y + -12.5 = 10.111874208 Simplifying y + -12.5 = 10.111874208 Reorder the terms: -12.5 + y = 10.111874208 Solving -12.5 + y = 10.111874208 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = 10.111874208 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = 10.111874208 + 12.5 y = 10.111874208 + 12.5 Combine like terms: 10.111874208 + 12.5 = 22.611874208 y = 22.611874208 Simplifying y = 22.611874208Subproblem 2
y + -12.5 = -10.111874208 Simplifying y + -12.5 = -10.111874208 Reorder the terms: -12.5 + y = -10.111874208 Solving -12.5 + y = -10.111874208 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + y = -10.111874208 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + y = -10.111874208 + 12.5 y = -10.111874208 + 12.5 Combine like terms: -10.111874208 + 12.5 = 2.388125792 y = 2.388125792 Simplifying y = 2.388125792Solution
The solution to the problem is based on the solutions from the subproblems. y = {22.611874208, 2.388125792}
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