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Simplifying y2 + -28y = -3 Reorder the terms: -28y + y2 = -3 Solving -28y + y2 = -3 Solving for variable 'y'. Reorder the terms: 3 + -28y + y2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -28y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -28y + -3 + y2 = 0 + -3 Reorder the terms: 3 + -3 + -28y + y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -28y + y2 = 0 + -3 -28y + y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -28y + y2 = -3 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 = -3 + 196 Reorder the terms: 196 + -28y + y2 = -3 + 196 Combine like terms: -3 + 196 = 193 196 + -28y + y2 = 193 Factor a perfect square on the left side: (y + -14)(y + -14) = 193 Calculate the square root of the right side: 13.892443989 Break this problem into two subproblems by setting (y + -14) equal to 13.892443989 and -13.892443989.Subproblem 1
y + -14 = 13.892443989 Simplifying y + -14 = 13.892443989 Reorder the terms: -14 + y = 13.892443989 Solving -14 + y = 13.892443989 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 = 13.892443989 + 14 Combine like terms: -14 + 14 = 0 0 + y = 13.892443989 + 14 y = 13.892443989 + 14 Combine like terms: 13.892443989 + 14 = 27.892443989 y = 27.892443989 Simplifying y = 27.892443989Subproblem 2
y + -14 = -13.892443989 Simplifying y + -14 = -13.892443989 Reorder the terms: -14 + y = -13.892443989 Solving -14 + y = -13.892443989 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 = -13.892443989 + 14 Combine like terms: -14 + 14 = 0 0 + y = -13.892443989 + 14 y = -13.892443989 + 14 Combine like terms: -13.892443989 + 14 = 0.107556011 y = 0.107556011 Simplifying y = 0.107556011Solution
The solution to the problem is based on the solutions from the subproblems. y = {27.892443989, 0.107556011}
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