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Simplifying 12.25y + y2 + -180 = 0 Reorder the terms: -180 + 12.25y + y2 = 0 Solving -180 + 12.25y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 12.25y + 180 + y2 = 0 + 180 Reorder the terms: -180 + 180 + 12.25y + y2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 12.25y + y2 = 0 + 180 12.25y + y2 = 0 + 180 Combine like terms: 0 + 180 = 180 12.25y + y2 = 180 The y term is 12.25y. Take half its coefficient (6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. 12.25y + 37.515625 + y2 = 180 + 37.515625 Reorder the terms: 37.515625 + 12.25y + y2 = 180 + 37.515625 Combine like terms: 180 + 37.515625 = 217.515625 37.515625 + 12.25y + y2 = 217.515625 Factor a perfect square on the left side: (y + 6.125)(y + 6.125) = 217.515625 Calculate the square root of the right side: 14.748410931 Break this problem into two subproblems by setting (y + 6.125) equal to 14.748410931 and -14.748410931.Subproblem 1
y + 6.125 = 14.748410931 Simplifying y + 6.125 = 14.748410931 Reorder the terms: 6.125 + y = 14.748410931 Solving 6.125 + y = 14.748410931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.125' to each side of the equation. 6.125 + -6.125 + y = 14.748410931 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + y = 14.748410931 + -6.125 y = 14.748410931 + -6.125 Combine like terms: 14.748410931 + -6.125 = 8.623410931 y = 8.623410931 Simplifying y = 8.623410931Subproblem 2
y + 6.125 = -14.748410931 Simplifying y + 6.125 = -14.748410931 Reorder the terms: 6.125 + y = -14.748410931 Solving 6.125 + y = -14.748410931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-6.125' to each side of the equation. 6.125 + -6.125 + y = -14.748410931 + -6.125 Combine like terms: 6.125 + -6.125 = 0.000 0.000 + y = -14.748410931 + -6.125 y = -14.748410931 + -6.125 Combine like terms: -14.748410931 + -6.125 = -20.873410931 y = -20.873410931 Simplifying y = -20.873410931Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.623410931, -20.873410931}
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