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Simplifying (3y2 + -4y + -5) + (8y2 + -2y + -1) = 0 Reorder the terms: (-5 + -4y + 3y2) + (8y2 + -2y + -1) = 0 Remove parenthesis around (-5 + -4y + 3y2) -5 + -4y + 3y2 + (8y2 + -2y + -1) = 0 Reorder the terms: -5 + -4y + 3y2 + (-1 + -2y + 8y2) = 0 Remove parenthesis around (-1 + -2y + 8y2) -5 + -4y + 3y2 + -1 + -2y + 8y2 = 0 Reorder the terms: -5 + -1 + -4y + -2y + 3y2 + 8y2 = 0 Combine like terms: -5 + -1 = -6 -6 + -4y + -2y + 3y2 + 8y2 = 0 Combine like terms: -4y + -2y = -6y -6 + -6y + 3y2 + 8y2 = 0 Combine like terms: 3y2 + 8y2 = 11y2 -6 + -6y + 11y2 = 0 Solving -6 + -6y + 11y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.5454545455 + -0.5454545455y + y2 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + -0.5454545455y + 0.5454545455 + y2 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + -0.5454545455y + y2 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + -0.5454545455y + y2 = 0 + 0.5454545455 -0.5454545455y + y2 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 -0.5454545455y + y2 = 0.5454545455 The y term is -0.5454545455y. Take half its coefficient (-0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. -0.5454545455y + 0.07438016533 + y2 = 0.5454545455 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455y + y2 = 0.5454545455 + 0.07438016533 Combine like terms: 0.5454545455 + 0.07438016533 = 0.61983471083 0.07438016533 + -0.5454545455y + y2 = 0.61983471083 Factor a perfect square on the left side: (y + -0.2727272728)(y + -0.2727272728) = 0.61983471083 Calculate the square root of the right side: 0.787295822 Break this problem into two subproblems by setting (y + -0.2727272728) equal to 0.787295822 and -0.787295822.Subproblem 1
y + -0.2727272728 = 0.787295822 Simplifying y + -0.2727272728 = 0.787295822 Reorder the terms: -0.2727272728 + y = 0.787295822 Solving -0.2727272728 + y = 0.787295822 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + y = 0.787295822 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + y = 0.787295822 + 0.2727272728 y = 0.787295822 + 0.2727272728 Combine like terms: 0.787295822 + 0.2727272728 = 1.0600230948 y = 1.0600230948 Simplifying y = 1.0600230948Subproblem 2
y + -0.2727272728 = -0.787295822 Simplifying y + -0.2727272728 = -0.787295822 Reorder the terms: -0.2727272728 + y = -0.787295822 Solving -0.2727272728 + y = -0.787295822 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + y = -0.787295822 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + y = -0.787295822 + 0.2727272728 y = -0.787295822 + 0.2727272728 Combine like terms: -0.787295822 + 0.2727272728 = -0.5145685492 y = -0.5145685492 Simplifying y = -0.5145685492Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.0600230948, -0.5145685492}
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