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Simplifying y2 + 28y + 37 = 0 Reorder the terms: 37 + 28y + y2 = 0 Solving 37 + 28y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 28y + -37 + y2 = 0 + -37 Reorder the terms: 37 + -37 + 28y + y2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 28y + y2 = 0 + -37 28y + y2 = 0 + -37 Combine like terms: 0 + -37 = -37 28y + y2 = -37 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 = -37 + 196 Reorder the terms: 196 + 28y + y2 = -37 + 196 Combine like terms: -37 + 196 = 159 196 + 28y + y2 = 159 Factor a perfect square on the left side: (y + 14)(y + 14) = 159 Calculate the square root of the right side: 12.609520213 Break this problem into two subproblems by setting (y + 14) equal to 12.609520213 and -12.609520213.Subproblem 1
y + 14 = 12.609520213 Simplifying y + 14 = 12.609520213 Reorder the terms: 14 + y = 12.609520213 Solving 14 + y = 12.609520213 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 = 12.609520213 + -14 Combine like terms: 14 + -14 = 0 0 + y = 12.609520213 + -14 y = 12.609520213 + -14 Combine like terms: 12.609520213 + -14 = -1.390479787 y = -1.390479787 Simplifying y = -1.390479787Subproblem 2
y + 14 = -12.609520213 Simplifying y + 14 = -12.609520213 Reorder the terms: 14 + y = -12.609520213 Solving 14 + y = -12.609520213 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 = -12.609520213 + -14 Combine like terms: 14 + -14 = 0 0 + y = -12.609520213 + -14 y = -12.609520213 + -14 Combine like terms: -12.609520213 + -14 = -26.609520213 y = -26.609520213 Simplifying y = -26.609520213Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.390479787, -26.609520213}
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