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Simplifying y2 + -40y + 60 = 0 Reorder the terms: 60 + -40y + y2 = 0 Solving 60 + -40y + 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 + -40y + -60 + y2 = 0 + -60 Reorder the terms: 60 + -60 + -40y + y2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -40y + y2 = 0 + -60 -40y + y2 = 0 + -60 Combine like terms: 0 + -60 = -60 -40y + y2 = -60 The y term is -40y. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40y + 400 + y2 = -60 + 400 Reorder the terms: 400 + -40y + y2 = -60 + 400 Combine like terms: -60 + 400 = 340 400 + -40y + y2 = 340 Factor a perfect square on the left side: (y + -20)(y + -20) = 340 Calculate the square root of the right side: 18.439088915 Break this problem into two subproblems by setting (y + -20) equal to 18.439088915 and -18.439088915.Subproblem 1
y + -20 = 18.439088915 Simplifying y + -20 = 18.439088915 Reorder the terms: -20 + y = 18.439088915 Solving -20 + y = 18.439088915 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + y = 18.439088915 + 20 Combine like terms: -20 + 20 = 0 0 + y = 18.439088915 + 20 y = 18.439088915 + 20 Combine like terms: 18.439088915 + 20 = 38.439088915 y = 38.439088915 Simplifying y = 38.439088915Subproblem 2
y + -20 = -18.439088915 Simplifying y + -20 = -18.439088915 Reorder the terms: -20 + y = -18.439088915 Solving -20 + y = -18.439088915 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + y = -18.439088915 + 20 Combine like terms: -20 + 20 = 0 0 + y = -18.439088915 + 20 y = -18.439088915 + 20 Combine like terms: -18.439088915 + 20 = 1.560911085 y = 1.560911085 Simplifying y = 1.560911085Solution
The solution to the problem is based on the solutions from the subproblems. y = {38.439088915, 1.560911085}
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