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Simplifying y2 + -17y + 71 = 0 Reorder the terms: 71 + -17y + y2 = 0 Solving 71 + -17y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-71' to each side of the equation. 71 + -17y + -71 + y2 = 0 + -71 Reorder the terms: 71 + -71 + -17y + y2 = 0 + -71 Combine like terms: 71 + -71 = 0 0 + -17y + y2 = 0 + -71 -17y + y2 = 0 + -71 Combine like terms: 0 + -71 = -71 -17y + y2 = -71 The y term is -17y. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17y + 72.25 + y2 = -71 + 72.25 Reorder the terms: 72.25 + -17y + y2 = -71 + 72.25 Combine like terms: -71 + 72.25 = 1.25 72.25 + -17y + y2 = 1.25 Factor a perfect square on the left side: (y + -8.5)(y + -8.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (y + -8.5) equal to 1.118033989 and -1.118033989.Subproblem 1
y + -8.5 = 1.118033989 Simplifying y + -8.5 = 1.118033989 Reorder the terms: -8.5 + y = 1.118033989 Solving -8.5 + y = 1.118033989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = 1.118033989 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = 1.118033989 + 8.5 y = 1.118033989 + 8.5 Combine like terms: 1.118033989 + 8.5 = 9.618033989 y = 9.618033989 Simplifying y = 9.618033989Subproblem 2
y + -8.5 = -1.118033989 Simplifying y + -8.5 = -1.118033989 Reorder the terms: -8.5 + y = -1.118033989 Solving -8.5 + y = -1.118033989 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = -1.118033989 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = -1.118033989 + 8.5 y = -1.118033989 + 8.5 Combine like terms: -1.118033989 + 8.5 = 7.381966011 y = 7.381966011 Simplifying y = 7.381966011Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.618033989, 7.381966011}
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