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Simplifying y2 + 57y + 57 = 0 Reorder the terms: 57 + 57y + y2 = 0 Solving 57 + 57y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-57' to each side of the equation. 57 + 57y + -57 + y2 = 0 + -57 Reorder the terms: 57 + -57 + 57y + y2 = 0 + -57 Combine like terms: 57 + -57 = 0 0 + 57y + y2 = 0 + -57 57y + y2 = 0 + -57 Combine like terms: 0 + -57 = -57 57y + y2 = -57 The y term is 57y. Take half its coefficient (28.5). Square it (812.25) and add it to both sides. Add '812.25' to each side of the equation. 57y + 812.25 + y2 = -57 + 812.25 Reorder the terms: 812.25 + 57y + y2 = -57 + 812.25 Combine like terms: -57 + 812.25 = 755.25 812.25 + 57y + y2 = 755.25 Factor a perfect square on the left side: (y + 28.5)(y + 28.5) = 755.25 Calculate the square root of the right side: 27.481812167 Break this problem into two subproblems by setting (y + 28.5) equal to 27.481812167 and -27.481812167.Subproblem 1
y + 28.5 = 27.481812167 Simplifying y + 28.5 = 27.481812167 Reorder the terms: 28.5 + y = 27.481812167 Solving 28.5 + y = 27.481812167 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-28.5' to each side of the equation. 28.5 + -28.5 + y = 27.481812167 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + y = 27.481812167 + -28.5 y = 27.481812167 + -28.5 Combine like terms: 27.481812167 + -28.5 = -1.018187833 y = -1.018187833 Simplifying y = -1.018187833Subproblem 2
y + 28.5 = -27.481812167 Simplifying y + 28.5 = -27.481812167 Reorder the terms: 28.5 + y = -27.481812167 Solving 28.5 + y = -27.481812167 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-28.5' to each side of the equation. 28.5 + -28.5 + y = -27.481812167 + -28.5 Combine like terms: 28.5 + -28.5 = 0.0 0.0 + y = -27.481812167 + -28.5 y = -27.481812167 + -28.5 Combine like terms: -27.481812167 + -28.5 = -55.981812167 y = -55.981812167 Simplifying y = -55.981812167Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.018187833, -55.981812167}
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