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Simplifying -2(5y + -1) + -1y = -4y(y + -3) Reorder the terms: -2(-1 + 5y) + -1y = -4y(y + -3) (-1 * -2 + 5y * -2) + -1y = -4y(y + -3) (2 + -10y) + -1y = -4y(y + -3) Combine like terms: -10y + -1y = -11y 2 + -11y = -4y(y + -3) Reorder the terms: 2 + -11y = -4y(-3 + y) 2 + -11y = (-3 * -4y + y * -4y) 2 + -11y = (12y + -4y2) Solving 2 + -11y = 12y + -4y2 Solving for variable 'y'. Combine like terms: -11y + -12y = -23y 2 + -23y + 4y2 = 12y + -4y2 + -12y + 4y2 Reorder the terms: 2 + -23y + 4y2 = 12y + -12y + -4y2 + 4y2 Combine like terms: 12y + -12y = 0 2 + -23y + 4y2 = 0 + -4y2 + 4y2 2 + -23y + 4y2 = -4y2 + 4y2 Combine like terms: -4y2 + 4y2 = 0 2 + -23y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -5.75y + y2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -5.75y + -0.5 + y2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -5.75y + y2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -5.75y + y2 = 0 + -0.5 -5.75y + y2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -5.75y + y2 = -0.5 The y term is -5.75y. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75y + 8.265625 + y2 = -0.5 + 8.265625 Reorder the terms: 8.265625 + -5.75y + y2 = -0.5 + 8.265625 Combine like terms: -0.5 + 8.265625 = 7.765625 8.265625 + -5.75y + y2 = 7.765625 Factor a perfect square on the left side: (y + -2.875)(y + -2.875) = 7.765625 Calculate the square root of the right side: 2.786687101 Break this problem into two subproblems by setting (y + -2.875) equal to 2.786687101 and -2.786687101.Subproblem 1
y + -2.875 = 2.786687101 Simplifying y + -2.875 = 2.786687101 Reorder the terms: -2.875 + y = 2.786687101 Solving -2.875 + y = 2.786687101 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + y = 2.786687101 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + y = 2.786687101 + 2.875 y = 2.786687101 + 2.875 Combine like terms: 2.786687101 + 2.875 = 5.661687101 y = 5.661687101 Simplifying y = 5.661687101Subproblem 2
y + -2.875 = -2.786687101 Simplifying y + -2.875 = -2.786687101 Reorder the terms: -2.875 + y = -2.786687101 Solving -2.875 + y = -2.786687101 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + y = -2.786687101 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + y = -2.786687101 + 2.875 y = -2.786687101 + 2.875 Combine like terms: -2.786687101 + 2.875 = 0.088312899 y = 0.088312899 Simplifying y = 0.088312899Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.661687101, 0.088312899}
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