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Simplifying 6y2 + 7y + -2 = 0 Reorder the terms: -2 + 7y + 6y2 = 0 Solving -2 + 7y + 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'. -0.3333333333 + 1.166666667y + y2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.166666667y + 0.3333333333 + y2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.166666667y + y2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.166666667y + y2 = 0 + 0.3333333333 1.166666667y + y2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.166666667y + y2 = 0.3333333333 The y term is 1.166666667y. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667y + 0.3402777780 + y2 = 0.3333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667y + y2 = 0.3333333333 + 0.3402777780 Combine like terms: 0.3333333333 + 0.3402777780 = 0.6736111113 0.3402777780 + 1.166666667y + y2 = 0.6736111113 Factor a perfect square on the left side: (y + 0.5833333335)(y + 0.5833333335) = 0.6736111113 Calculate the square root of the right side: 0.82073815 Break this problem into two subproblems by setting (y + 0.5833333335) equal to 0.82073815 and -0.82073815.Subproblem 1
y + 0.5833333335 = 0.82073815 Simplifying y + 0.5833333335 = 0.82073815 Reorder the terms: 0.5833333335 + y = 0.82073815 Solving 0.5833333335 + y = 0.82073815 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + y = 0.82073815 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + y = 0.82073815 + -0.5833333335 y = 0.82073815 + -0.5833333335 Combine like terms: 0.82073815 + -0.5833333335 = 0.2374048165 y = 0.2374048165 Simplifying y = 0.2374048165Subproblem 2
y + 0.5833333335 = -0.82073815 Simplifying y + 0.5833333335 = -0.82073815 Reorder the terms: 0.5833333335 + y = -0.82073815 Solving 0.5833333335 + y = -0.82073815 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + y = -0.82073815 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + y = -0.82073815 + -0.5833333335 y = -0.82073815 + -0.5833333335 Combine like terms: -0.82073815 + -0.5833333335 = -1.4040714835 y = -1.4040714835 Simplifying y = -1.4040714835Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.2374048165, -1.4040714835}
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