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Simplifying -10y2 + 35y + 57 = 0 Reorder the terms: 57 + 35y + -10y2 = 0 Solving 57 + 35y + -10y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -5.7 + -3.5y + y2 = 0 Move the constant term to the right: Add '5.7' to each side of the equation. -5.7 + -3.5y + 5.7 + y2 = 0 + 5.7 Reorder the terms: -5.7 + 5.7 + -3.5y + y2 = 0 + 5.7 Combine like terms: -5.7 + 5.7 = 0.0 0.0 + -3.5y + y2 = 0 + 5.7 -3.5y + y2 = 0 + 5.7 Combine like terms: 0 + 5.7 = 5.7 -3.5y + y2 = 5.7 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = 5.7 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = 5.7 + 3.0625 Combine like terms: 5.7 + 3.0625 = 8.7625 3.0625 + -3.5y + y2 = 8.7625 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = 8.7625 Calculate the square root of the right side: 2.960152023 Break this problem into two subproblems by setting (y + -1.75) equal to 2.960152023 and -2.960152023.Subproblem 1
y + -1.75 = 2.960152023 Simplifying y + -1.75 = 2.960152023 Reorder the terms: -1.75 + y = 2.960152023 Solving -1.75 + y = 2.960152023 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 2.960152023 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 2.960152023 + 1.75 y = 2.960152023 + 1.75 Combine like terms: 2.960152023 + 1.75 = 4.710152023 y = 4.710152023 Simplifying y = 4.710152023Subproblem 2
y + -1.75 = -2.960152023 Simplifying y + -1.75 = -2.960152023 Reorder the terms: -1.75 + y = -2.960152023 Solving -1.75 + y = -2.960152023 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -2.960152023 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -2.960152023 + 1.75 y = -2.960152023 + 1.75 Combine like terms: -2.960152023 + 1.75 = -1.210152023 y = -1.210152023 Simplifying y = -1.210152023Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.710152023, -1.210152023}
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