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Simplifying 6y2 + 127y + 5 = 0 Reorder the terms: 5 + 127y + 6y2 = 0 Solving 5 + 127y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.8333333333 + 21.16666667y + y2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + 21.16666667y + -0.8333333333 + y2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + 21.16666667y + y2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + 21.16666667y + y2 = 0 + -0.8333333333 21.16666667y + y2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 21.16666667y + y2 = -0.8333333333 The y term is 21.16666667y. Take half its coefficient (10.58333334). Square it (112.0069446) and add it to both sides. Add '112.0069446' to each side of the equation. 21.16666667y + 112.0069446 + y2 = -0.8333333333 + 112.0069446 Reorder the terms: 112.0069446 + 21.16666667y + y2 = -0.8333333333 + 112.0069446 Combine like terms: -0.8333333333 + 112.0069446 = 111.1736112667 112.0069446 + 21.16666667y + y2 = 111.1736112667 Factor a perfect square on the left side: (y + 10.58333334)(y + 10.58333334) = 111.1736112667 Calculate the square root of the right side: 10.54388976 Break this problem into two subproblems by setting (y + 10.58333334) equal to 10.54388976 and -10.54388976.Subproblem 1
y + 10.58333334 = 10.54388976 Simplifying y + 10.58333334 = 10.54388976 Reorder the terms: 10.58333334 + y = 10.54388976 Solving 10.58333334 + y = 10.54388976 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10.58333334' to each side of the equation. 10.58333334 + -10.58333334 + y = 10.54388976 + -10.58333334 Combine like terms: 10.58333334 + -10.58333334 = 0.00000000 0.00000000 + y = 10.54388976 + -10.58333334 y = 10.54388976 + -10.58333334 Combine like terms: 10.54388976 + -10.58333334 = -0.03944358 y = -0.03944358 Simplifying y = -0.03944358Subproblem 2
y + 10.58333334 = -10.54388976 Simplifying y + 10.58333334 = -10.54388976 Reorder the terms: 10.58333334 + y = -10.54388976 Solving 10.58333334 + y = -10.54388976 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10.58333334' to each side of the equation. 10.58333334 + -10.58333334 + y = -10.54388976 + -10.58333334 Combine like terms: 10.58333334 + -10.58333334 = 0.00000000 0.00000000 + y = -10.54388976 + -10.58333334 y = -10.54388976 + -10.58333334 Combine like terms: -10.54388976 + -10.58333334 = -21.1272231 y = -21.1272231 Simplifying y = -21.1272231Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.03944358, -21.1272231}
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