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Simplifying 27y2 + 3y + -98 = 0 Reorder the terms: -98 + 3y + 27y2 = 0 Solving -98 + 3y + 27y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -3.62962963 + 0.1111111111y + y2 = 0 Move the constant term to the right: Add '3.62962963' to each side of the equation. -3.62962963 + 0.1111111111y + 3.62962963 + y2 = 0 + 3.62962963 Reorder the terms: -3.62962963 + 3.62962963 + 0.1111111111y + y2 = 0 + 3.62962963 Combine like terms: -3.62962963 + 3.62962963 = 0.00000000 0.00000000 + 0.1111111111y + y2 = 0 + 3.62962963 0.1111111111y + y2 = 0 + 3.62962963 Combine like terms: 0 + 3.62962963 = 3.62962963 0.1111111111y + y2 = 3.62962963 The y term is 0.1111111111y. Take half its coefficient (0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. 0.1111111111y + 0.003086419752 + y2 = 3.62962963 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111y + y2 = 3.62962963 + 0.003086419752 Combine like terms: 3.62962963 + 0.003086419752 = 3.632716049752 0.003086419752 + 0.1111111111y + y2 = 3.632716049752 Factor a perfect square on the left side: (y + 0.05555555555)(y + 0.05555555555) = 3.632716049752 Calculate the square root of the right side: 1.905968533 Break this problem into two subproblems by setting (y + 0.05555555555) equal to 1.905968533 and -1.905968533.Subproblem 1
y + 0.05555555555 = 1.905968533 Simplifying y + 0.05555555555 = 1.905968533 Reorder the terms: 0.05555555555 + y = 1.905968533 Solving 0.05555555555 + y = 1.905968533 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + y = 1.905968533 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + y = 1.905968533 + -0.05555555555 y = 1.905968533 + -0.05555555555 Combine like terms: 1.905968533 + -0.05555555555 = 1.85041297745 y = 1.85041297745 Simplifying y = 1.85041297745Subproblem 2
y + 0.05555555555 = -1.905968533 Simplifying y + 0.05555555555 = -1.905968533 Reorder the terms: 0.05555555555 + y = -1.905968533 Solving 0.05555555555 + y = -1.905968533 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + y = -1.905968533 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + y = -1.905968533 + -0.05555555555 y = -1.905968533 + -0.05555555555 Combine like terms: -1.905968533 + -0.05555555555 = -1.96152408855 y = -1.96152408855 Simplifying y = -1.96152408855Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.85041297745, -1.96152408855}
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