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Simplifying 16y2 + -149y + -102 = 0 Reorder the terms: -102 + -149y + 16y2 = 0 Solving -102 + -149y + 16y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.375 + -9.3125y + y2 = 0 Move the constant term to the right: Add '6.375' to each side of the equation. -6.375 + -9.3125y + 6.375 + y2 = 0 + 6.375 Reorder the terms: -6.375 + 6.375 + -9.3125y + y2 = 0 + 6.375 Combine like terms: -6.375 + 6.375 = 0.000 0.000 + -9.3125y + y2 = 0 + 6.375 -9.3125y + y2 = 0 + 6.375 Combine like terms: 0 + 6.375 = 6.375 -9.3125y + y2 = 6.375 The y term is -9.3125y. Take half its coefficient (-4.65625). Square it (21.68066406) and add it to both sides. Add '21.68066406' to each side of the equation. -9.3125y + 21.68066406 + y2 = 6.375 + 21.68066406 Reorder the terms: 21.68066406 + -9.3125y + y2 = 6.375 + 21.68066406 Combine like terms: 6.375 + 21.68066406 = 28.05566406 21.68066406 + -9.3125y + y2 = 28.05566406 Factor a perfect square on the left side: (y + -4.65625)(y + -4.65625) = 28.05566406 Calculate the square root of the right side: 5.29675977 Break this problem into two subproblems by setting (y + -4.65625) equal to 5.29675977 and -5.29675977.Subproblem 1
y + -4.65625 = 5.29675977 Simplifying y + -4.65625 = 5.29675977 Reorder the terms: -4.65625 + y = 5.29675977 Solving -4.65625 + y = 5.29675977 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.65625' to each side of the equation. -4.65625 + 4.65625 + y = 5.29675977 + 4.65625 Combine like terms: -4.65625 + 4.65625 = 0.00000 0.00000 + y = 5.29675977 + 4.65625 y = 5.29675977 + 4.65625 Combine like terms: 5.29675977 + 4.65625 = 9.95300977 y = 9.95300977 Simplifying y = 9.95300977Subproblem 2
y + -4.65625 = -5.29675977 Simplifying y + -4.65625 = -5.29675977 Reorder the terms: -4.65625 + y = -5.29675977 Solving -4.65625 + y = -5.29675977 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.65625' to each side of the equation. -4.65625 + 4.65625 + y = -5.29675977 + 4.65625 Combine like terms: -4.65625 + 4.65625 = 0.00000 0.00000 + y = -5.29675977 + 4.65625 y = -5.29675977 + 4.65625 Combine like terms: -5.29675977 + 4.65625 = -0.64050977 y = -0.64050977 Simplifying y = -0.64050977Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.95300977, -0.64050977}
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