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Simplifying 36y2 + 371y + 890 = 0 Reorder the terms: 890 + 371y + 36y2 = 0 Solving 890 + 371y + 36y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 24.72222222 + 10.30555556y + y2 = 0 Move the constant term to the right: Add '-24.72222222' to each side of the equation. 24.72222222 + 10.30555556y + -24.72222222 + y2 = 0 + -24.72222222 Reorder the terms: 24.72222222 + -24.72222222 + 10.30555556y + y2 = 0 + -24.72222222 Combine like terms: 24.72222222 + -24.72222222 = 0.00000000 0.00000000 + 10.30555556y + y2 = 0 + -24.72222222 10.30555556y + y2 = 0 + -24.72222222 Combine like terms: 0 + -24.72222222 = -24.72222222 10.30555556y + y2 = -24.72222222 The y term is 10.30555556y. Take half its coefficient (5.15277778). Square it (26.55111885) and add it to both sides. Add '26.55111885' to each side of the equation. 10.30555556y + 26.55111885 + y2 = -24.72222222 + 26.55111885 Reorder the terms: 26.55111885 + 10.30555556y + y2 = -24.72222222 + 26.55111885 Combine like terms: -24.72222222 + 26.55111885 = 1.82889663 26.55111885 + 10.30555556y + y2 = 1.82889663 Factor a perfect square on the left side: (y + 5.15277778)(y + 5.15277778) = 1.82889663 Calculate the square root of the right side: 1.352367047 Break this problem into two subproblems by setting (y + 5.15277778) equal to 1.352367047 and -1.352367047.Subproblem 1
y + 5.15277778 = 1.352367047 Simplifying y + 5.15277778 = 1.352367047 Reorder the terms: 5.15277778 + y = 1.352367047 Solving 5.15277778 + y = 1.352367047 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.15277778' to each side of the equation. 5.15277778 + -5.15277778 + y = 1.352367047 + -5.15277778 Combine like terms: 5.15277778 + -5.15277778 = 0.00000000 0.00000000 + y = 1.352367047 + -5.15277778 y = 1.352367047 + -5.15277778 Combine like terms: 1.352367047 + -5.15277778 = -3.800410733 y = -3.800410733 Simplifying y = -3.800410733Subproblem 2
y + 5.15277778 = -1.352367047 Simplifying y + 5.15277778 = -1.352367047 Reorder the terms: 5.15277778 + y = -1.352367047 Solving 5.15277778 + y = -1.352367047 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5.15277778' to each side of the equation. 5.15277778 + -5.15277778 + y = -1.352367047 + -5.15277778 Combine like terms: 5.15277778 + -5.15277778 = 0.00000000 0.00000000 + y = -1.352367047 + -5.15277778 y = -1.352367047 + -5.15277778 Combine like terms: -1.352367047 + -5.15277778 = -6.505144827 y = -6.505144827 Simplifying y = -6.505144827Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.800410733, -6.505144827}
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