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Simplifying 0 = y2 + 28y + -25 Reorder the terms: 0 = -25 + 28y + y2 Solving 0 = -25 + 28y + y2 Solving for variable 'y'. Combine like terms: 0 + 25 = 25 25 + -28y + -1y2 = -25 + 28y + y2 + 25 + -28y + -1y2 Reorder the terms: 25 + -28y + -1y2 = -25 + 25 + 28y + -28y + y2 + -1y2 Combine like terms: -25 + 25 = 0 25 + -28y + -1y2 = 0 + 28y + -28y + y2 + -1y2 25 + -28y + -1y2 = 28y + -28y + y2 + -1y2 Combine like terms: 28y + -28y = 0 25 + -28y + -1y2 = 0 + y2 + -1y2 25 + -28y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 25 + -28y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 28y + y2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 28y + 25 + y2 = 0 + 25 Reorder the terms: -25 + 25 + 28y + y2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 28y + y2 = 0 + 25 28y + y2 = 0 + 25 Combine like terms: 0 + 25 = 25 28y + y2 = 25 The y term is 28y. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28y + 196 + y2 = 25 + 196 Reorder the terms: 196 + 28y + y2 = 25 + 196 Combine like terms: 25 + 196 = 221 196 + 28y + y2 = 221 Factor a perfect square on the left side: (y + 14)(y + 14) = 221 Calculate the square root of the right side: 14.866068747 Break this problem into two subproblems by setting (y + 14) equal to 14.866068747 and -14.866068747.Subproblem 1
y + 14 = 14.866068747 Simplifying y + 14 = 14.866068747 Reorder the terms: 14 + y = 14.866068747 Solving 14 + y = 14.866068747 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = 14.866068747 + -14 Combine like terms: 14 + -14 = 0 0 + y = 14.866068747 + -14 y = 14.866068747 + -14 Combine like terms: 14.866068747 + -14 = 0.866068747 y = 0.866068747 Simplifying y = 0.866068747Subproblem 2
y + 14 = -14.866068747 Simplifying y + 14 = -14.866068747 Reorder the terms: 14 + y = -14.866068747 Solving 14 + y = -14.866068747 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = -14.866068747 + -14 Combine like terms: 14 + -14 = 0 0 + y = -14.866068747 + -14 y = -14.866068747 + -14 Combine like terms: -14.866068747 + -14 = -28.866068747 y = -28.866068747 Simplifying y = -28.866068747Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.866068747, -28.866068747}
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