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Simplifying -1y2 + -25y + 45 = 0 Reorder the terms: 45 + -25y + -1y2 = 0 Solving 45 + -25y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + 25y + y2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 25y + 45 + y2 = 0 + 45 Reorder the terms: -45 + 45 + 25y + y2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 25y + y2 = 0 + 45 25y + y2 = 0 + 45 Combine like terms: 0 + 45 = 45 25y + y2 = 45 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 = 45 + 156.25 Reorder the terms: 156.25 + 25y + y2 = 45 + 156.25 Combine like terms: 45 + 156.25 = 201.25 156.25 + 25y + y2 = 201.25 Factor a perfect square on the left side: (y + 12.5)(y + 12.5) = 201.25 Calculate the square root of the right side: 14.186260959 Break this problem into two subproblems by setting (y + 12.5) equal to 14.186260959 and -14.186260959.Subproblem 1
y + 12.5 = 14.186260959 Simplifying y + 12.5 = 14.186260959 Reorder the terms: 12.5 + y = 14.186260959 Solving 12.5 + y = 14.186260959 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 = 14.186260959 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + y = 14.186260959 + -12.5 y = 14.186260959 + -12.5 Combine like terms: 14.186260959 + -12.5 = 1.686260959 y = 1.686260959 Simplifying y = 1.686260959Subproblem 2
y + 12.5 = -14.186260959 Simplifying y + 12.5 = -14.186260959 Reorder the terms: 12.5 + y = -14.186260959 Solving 12.5 + y = -14.186260959 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 = -14.186260959 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + y = -14.186260959 + -12.5 y = -14.186260959 + -12.5 Combine like terms: -14.186260959 + -12.5 = -26.686260959 y = -26.686260959 Simplifying y = -26.686260959Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.686260959, -26.686260959}
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