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Simplifying 2y2 + -17y + -1 = 0 Reorder the terms: -1 + -17y + 2y2 = 0 Solving -1 + -17y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -8.5y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -8.5y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -8.5y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -8.5y + y2 = 0 + 0.5 -8.5y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -8.5y + y2 = 0.5 The y term is -8.5y. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5y + 18.0625 + y2 = 0.5 + 18.0625 Reorder the terms: 18.0625 + -8.5y + y2 = 0.5 + 18.0625 Combine like terms: 0.5 + 18.0625 = 18.5625 18.0625 + -8.5y + y2 = 18.5625 Factor a perfect square on the left side: (y + -4.25)(y + -4.25) = 18.5625 Calculate the square root of the right side: 4.308421985 Break this problem into two subproblems by setting (y + -4.25) equal to 4.308421985 and -4.308421985.Subproblem 1
y + -4.25 = 4.308421985 Simplifying y + -4.25 = 4.308421985 Reorder the terms: -4.25 + y = 4.308421985 Solving -4.25 + y = 4.308421985 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + y = 4.308421985 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + y = 4.308421985 + 4.25 y = 4.308421985 + 4.25 Combine like terms: 4.308421985 + 4.25 = 8.558421985 y = 8.558421985 Simplifying y = 8.558421985Subproblem 2
y + -4.25 = -4.308421985 Simplifying y + -4.25 = -4.308421985 Reorder the terms: -4.25 + y = -4.308421985 Solving -4.25 + y = -4.308421985 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + y = -4.308421985 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + y = -4.308421985 + 4.25 y = -4.308421985 + 4.25 Combine like terms: -4.308421985 + 4.25 = -0.058421985 y = -0.058421985 Simplifying y = -0.058421985Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.558421985, -0.058421985}
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