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Simplifying y2 + -34y + 165 = 0 Reorder the terms: 165 + -34y + y2 = 0 Solving 165 + -34y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-165' to each side of the equation. 165 + -34y + -165 + y2 = 0 + -165 Reorder the terms: 165 + -165 + -34y + y2 = 0 + -165 Combine like terms: 165 + -165 = 0 0 + -34y + y2 = 0 + -165 -34y + y2 = 0 + -165 Combine like terms: 0 + -165 = -165 -34y + y2 = -165 The y term is -34y. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34y + 289 + y2 = -165 + 289 Reorder the terms: 289 + -34y + y2 = -165 + 289 Combine like terms: -165 + 289 = 124 289 + -34y + y2 = 124 Factor a perfect square on the left side: (y + -17)(y + -17) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (y + -17) equal to 11.135528726 and -11.135528726.Subproblem 1
y + -17 = 11.135528726 Simplifying y + -17 = 11.135528726 Reorder the terms: -17 + y = 11.135528726 Solving -17 + y = 11.135528726 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + y = 11.135528726 + 17 Combine like terms: -17 + 17 = 0 0 + y = 11.135528726 + 17 y = 11.135528726 + 17 Combine like terms: 11.135528726 + 17 = 28.135528726 y = 28.135528726 Simplifying y = 28.135528726Subproblem 2
y + -17 = -11.135528726 Simplifying y + -17 = -11.135528726 Reorder the terms: -17 + y = -11.135528726 Solving -17 + y = -11.135528726 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + y = -11.135528726 + 17 Combine like terms: -17 + 17 = 0 0 + y = -11.135528726 + 17 y = -11.135528726 + 17 Combine like terms: -11.135528726 + 17 = 5.864471274 y = 5.864471274 Simplifying y = 5.864471274Solution
The solution to the problem is based on the solutions from the subproblems. y = {28.135528726, 5.864471274}
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