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Simplifying y2 + -19y + -60 = 0 Reorder the terms: -60 + -19y + y2 = 0 Solving -60 + -19y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -19y + 60 + y2 = 0 + 60 Reorder the terms: -60 + 60 + -19y + y2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -19y + y2 = 0 + 60 -19y + y2 = 0 + 60 Combine like terms: 0 + 60 = 60 -19y + y2 = 60 The y term is -19y. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19y + 90.25 + y2 = 60 + 90.25 Reorder the terms: 90.25 + -19y + y2 = 60 + 90.25 Combine like terms: 60 + 90.25 = 150.25 90.25 + -19y + y2 = 150.25 Factor a perfect square on the left side: (y + -9.5)(y + -9.5) = 150.25 Calculate the square root of the right side: 12.257650672 Break this problem into two subproblems by setting (y + -9.5) equal to 12.257650672 and -12.257650672.Subproblem 1
y + -9.5 = 12.257650672 Simplifying y + -9.5 = 12.257650672 Reorder the terms: -9.5 + y = 12.257650672 Solving -9.5 + y = 12.257650672 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = 12.257650672 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = 12.257650672 + 9.5 y = 12.257650672 + 9.5 Combine like terms: 12.257650672 + 9.5 = 21.757650672 y = 21.757650672 Simplifying y = 21.757650672Subproblem 2
y + -9.5 = -12.257650672 Simplifying y + -9.5 = -12.257650672 Reorder the terms: -9.5 + y = -12.257650672 Solving -9.5 + y = -12.257650672 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = -12.257650672 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = -12.257650672 + 9.5 y = -12.257650672 + 9.5 Combine like terms: -12.257650672 + 9.5 = -2.757650672 y = -2.757650672 Simplifying y = -2.757650672Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.757650672, -2.757650672}
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