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Simplifying 5(-3y + -1) + -1(6 + -5y) * y = -6 Reorder the terms: 5(-1 + -3y) + -1(6 + -5y) * y = -6 (-1 * 5 + -3y * 5) + -1(6 + -5y) * y = -6 (-5 + -15y) + -1(6 + -5y) * y = -6 Reorder the terms for easier multiplication: -5 + -15y + -1y(6 + -5y) = -6 -5 + -15y + (6 * -1y + -5y * -1y) = -6 -5 + -15y + (-6y + 5y2) = -6 Combine like terms: -15y + -6y = -21y -5 + -21y + 5y2 = -6 Solving -5 + -21y + 5y2 = -6 Solving for variable 'y'. Reorder the terms: -5 + 6 + -21y + 5y2 = -6 + 6 Combine like terms: -5 + 6 = 1 1 + -21y + 5y2 = -6 + 6 Combine like terms: -6 + 6 = 0 1 + -21y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -4.2y + y2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -4.2y + -0.2 + y2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -4.2y + y2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -4.2y + y2 = 0 + -0.2 -4.2y + y2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -4.2y + y2 = -0.2 The y term is -4.2y. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2y + 4.41 + y2 = -0.2 + 4.41 Reorder the terms: 4.41 + -4.2y + y2 = -0.2 + 4.41 Combine like terms: -0.2 + 4.41 = 4.21 4.41 + -4.2y + y2 = 4.21 Factor a perfect square on the left side: (y + -2.1)(y + -2.1) = 4.21 Calculate the square root of the right side: 2.051828453 Break this problem into two subproblems by setting (y + -2.1) equal to 2.051828453 and -2.051828453.Subproblem 1
y + -2.1 = 2.051828453 Simplifying y + -2.1 = 2.051828453 Reorder the terms: -2.1 + y = 2.051828453 Solving -2.1 + y = 2.051828453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + y = 2.051828453 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + y = 2.051828453 + 2.1 y = 2.051828453 + 2.1 Combine like terms: 2.051828453 + 2.1 = 4.151828453 y = 4.151828453 Simplifying y = 4.151828453Subproblem 2
y + -2.1 = -2.051828453 Simplifying y + -2.1 = -2.051828453 Reorder the terms: -2.1 + y = -2.051828453 Solving -2.1 + y = -2.051828453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + y = -2.051828453 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + y = -2.051828453 + 2.1 y = -2.051828453 + 2.1 Combine like terms: -2.051828453 + 2.1 = 0.048171547 y = 0.048171547 Simplifying y = 0.048171547Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.151828453, 0.048171547}
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