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Simplifying -2(6y + -10) + -1y = -4y(y + -5) Reorder the terms: -2(-10 + 6y) + -1y = -4y(y + -5) (-10 * -2 + 6y * -2) + -1y = -4y(y + -5) (20 + -12y) + -1y = -4y(y + -5) Combine like terms: -12y + -1y = -13y 20 + -13y = -4y(y + -5) Reorder the terms: 20 + -13y = -4y(-5 + y) 20 + -13y = (-5 * -4y + y * -4y) 20 + -13y = (20y + -4y2) Solving 20 + -13y = 20y + -4y2 Solving for variable 'y'. Combine like terms: -13y + -20y = -33y 20 + -33y + 4y2 = 20y + -4y2 + -20y + 4y2 Reorder the terms: 20 + -33y + 4y2 = 20y + -20y + -4y2 + 4y2 Combine like terms: 20y + -20y = 0 20 + -33y + 4y2 = 0 + -4y2 + 4y2 20 + -33y + 4y2 = -4y2 + 4y2 Combine like terms: -4y2 + 4y2 = 0 20 + -33y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5 + -8.25y + y2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8.25y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -8.25y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8.25y + y2 = 0 + -5 -8.25y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8.25y + y2 = -5 The y term is -8.25y. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25y + 17.015625 + y2 = -5 + 17.015625 Reorder the terms: 17.015625 + -8.25y + y2 = -5 + 17.015625 Combine like terms: -5 + 17.015625 = 12.015625 17.015625 + -8.25y + y2 = 12.015625 Factor a perfect square on the left side: (y + -4.125)(y + -4.125) = 12.015625 Calculate the square root of the right side: 3.466356156 Break this problem into two subproblems by setting (y + -4.125) equal to 3.466356156 and -3.466356156.Subproblem 1
y + -4.125 = 3.466356156 Simplifying y + -4.125 = 3.466356156 Reorder the terms: -4.125 + y = 3.466356156 Solving -4.125 + y = 3.466356156 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + y = 3.466356156 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + y = 3.466356156 + 4.125 y = 3.466356156 + 4.125 Combine like terms: 3.466356156 + 4.125 = 7.591356156 y = 7.591356156 Simplifying y = 7.591356156Subproblem 2
y + -4.125 = -3.466356156 Simplifying y + -4.125 = -3.466356156 Reorder the terms: -4.125 + y = -3.466356156 Solving -4.125 + y = -3.466356156 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + y = -3.466356156 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + y = -3.466356156 + 4.125 y = -3.466356156 + 4.125 Combine like terms: -3.466356156 + 4.125 = 0.658643844 y = 0.658643844 Simplifying y = 0.658643844Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.591356156, 0.658643844}
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