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Simplifying 18y2 + -33y + 10 = 0 Reorder the terms: 10 + -33y + 18y2 = 0 Solving 10 + -33y + 18y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.5555555556 + -1.833333333y + y2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -1.833333333y + -0.5555555556 + y2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -1.833333333y + y2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -1.833333333y + y2 = 0 + -0.5555555556 -1.833333333y + y2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -1.833333333y + y2 = -0.5555555556 The y term is -1.833333333y. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333y + 0.8402777775 + y2 = -0.5555555556 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333y + y2 = -0.5555555556 + 0.8402777775 Combine like terms: -0.5555555556 + 0.8402777775 = 0.2847222219 0.8402777775 + -1.833333333y + y2 = 0.2847222219 Factor a perfect square on the left side: (y + -0.9166666665)(y + -0.9166666665) = 0.2847222219 Calculate the square root of the right side: 0.533593686 Break this problem into two subproblems by setting (y + -0.9166666665) equal to 0.533593686 and -0.533593686.Subproblem 1
y + -0.9166666665 = 0.533593686 Simplifying y + -0.9166666665 = 0.533593686 Reorder the terms: -0.9166666665 + y = 0.533593686 Solving -0.9166666665 + y = 0.533593686 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + y = 0.533593686 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + y = 0.533593686 + 0.9166666665 y = 0.533593686 + 0.9166666665 Combine like terms: 0.533593686 + 0.9166666665 = 1.4502603525 y = 1.4502603525 Simplifying y = 1.4502603525Subproblem 2
y + -0.9166666665 = -0.533593686 Simplifying y + -0.9166666665 = -0.533593686 Reorder the terms: -0.9166666665 + y = -0.533593686 Solving -0.9166666665 + y = -0.533593686 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + y = -0.533593686 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + y = -0.533593686 + 0.9166666665 y = -0.533593686 + 0.9166666665 Combine like terms: -0.533593686 + 0.9166666665 = 0.3830729805 y = 0.3830729805 Simplifying y = 0.3830729805Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.4502603525, 0.3830729805}
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