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Simplifying 6y2 + 7y + -45 = 0 Reorder the terms: -45 + 7y + 6y2 = 0 Solving -45 + 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'. -7.5 + 1.166666667y + y2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 1.166666667y + 7.5 + y2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 1.166666667y + y2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 1.166666667y + y2 = 0 + 7.5 1.166666667y + y2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 1.166666667y + y2 = 7.5 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 = 7.5 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667y + y2 = 7.5 + 0.3402777780 Combine like terms: 7.5 + 0.3402777780 = 7.840277778 0.3402777780 + 1.166666667y + y2 = 7.840277778 Factor a perfect square on the left side: (y + 0.5833333335)(y + 0.5833333335) = 7.840277778 Calculate the square root of the right side: 2.800049603 Break this problem into two subproblems by setting (y + 0.5833333335) equal to 2.800049603 and -2.800049603.Subproblem 1
y + 0.5833333335 = 2.800049603 Simplifying y + 0.5833333335 = 2.800049603 Reorder the terms: 0.5833333335 + y = 2.800049603 Solving 0.5833333335 + y = 2.800049603 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 = 2.800049603 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + y = 2.800049603 + -0.5833333335 y = 2.800049603 + -0.5833333335 Combine like terms: 2.800049603 + -0.5833333335 = 2.2167162695 y = 2.2167162695 Simplifying y = 2.2167162695Subproblem 2
y + 0.5833333335 = -2.800049603 Simplifying y + 0.5833333335 = -2.800049603 Reorder the terms: 0.5833333335 + y = -2.800049603 Solving 0.5833333335 + y = -2.800049603 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 = -2.800049603 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + y = -2.800049603 + -0.5833333335 y = -2.800049603 + -0.5833333335 Combine like terms: -2.800049603 + -0.5833333335 = -3.3833829365 y = -3.3833829365 Simplifying y = -3.3833829365Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.2167162695, -3.3833829365}
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