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Simplifying y2 + -26y + -55 = 0 Reorder the terms: -55 + -26y + y2 = 0 Solving -55 + -26y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + -26y + 55 + y2 = 0 + 55 Reorder the terms: -55 + 55 + -26y + y2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -26y + y2 = 0 + 55 -26y + y2 = 0 + 55 Combine like terms: 0 + 55 = 55 -26y + y2 = 55 The y term is -26y. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26y + 169 + y2 = 55 + 169 Reorder the terms: 169 + -26y + y2 = 55 + 169 Combine like terms: 55 + 169 = 224 169 + -26y + y2 = 224 Factor a perfect square on the left side: (y + -13)(y + -13) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (y + -13) equal to 14.966629547 and -14.966629547.Subproblem 1
y + -13 = 14.966629547 Simplifying y + -13 = 14.966629547 Reorder the terms: -13 + y = 14.966629547 Solving -13 + y = 14.966629547 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + y = 14.966629547 + 13 Combine like terms: -13 + 13 = 0 0 + y = 14.966629547 + 13 y = 14.966629547 + 13 Combine like terms: 14.966629547 + 13 = 27.966629547 y = 27.966629547 Simplifying y = 27.966629547Subproblem 2
y + -13 = -14.966629547 Simplifying y + -13 = -14.966629547 Reorder the terms: -13 + y = -14.966629547 Solving -13 + y = -14.966629547 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + y = -14.966629547 + 13 Combine like terms: -13 + 13 = 0 0 + y = -14.966629547 + 13 y = -14.966629547 + 13 Combine like terms: -14.966629547 + 13 = -1.966629547 y = -1.966629547 Simplifying y = -1.966629547Solution
The solution to the problem is based on the solutions from the subproblems. y = {27.966629547, -1.966629547}
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