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Simplifying (2y2 + -1y + -4) + (7y2 + -6y + 5) = 0 Reorder the terms: (-4 + -1y + 2y2) + (7y2 + -6y + 5) = 0 Remove parenthesis around (-4 + -1y + 2y2) -4 + -1y + 2y2 + (7y2 + -6y + 5) = 0 Reorder the terms: -4 + -1y + 2y2 + (5 + -6y + 7y2) = 0 Remove parenthesis around (5 + -6y + 7y2) -4 + -1y + 2y2 + 5 + -6y + 7y2 = 0 Reorder the terms: -4 + 5 + -1y + -6y + 2y2 + 7y2 = 0 Combine like terms: -4 + 5 = 1 1 + -1y + -6y + 2y2 + 7y2 = 0 Combine like terms: -1y + -6y = -7y 1 + -7y + 2y2 + 7y2 = 0 Combine like terms: 2y2 + 7y2 = 9y2 1 + -7y + 9y2 = 0 Solving 1 + -7y + 9y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + -0.7777777778y + y2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.7777777778y + -0.1111111111 + y2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + -0.7777777778y + y2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + -0.7777777778y + y2 = 0 + -0.1111111111 -0.7777777778y + y2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 -0.7777777778y + y2 = -0.1111111111 The y term is -0.7777777778y. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778y + 0.1512345679 + y2 = -0.1111111111 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778y + y2 = -0.1111111111 + 0.1512345679 Combine like terms: -0.1111111111 + 0.1512345679 = 0.0401234568 0.1512345679 + -0.7777777778y + y2 = 0.0401234568 Factor a perfect square on the left side: (y + -0.3888888889)(y + -0.3888888889) = 0.0401234568 Calculate the square root of the right side: 0.200308404 Break this problem into two subproblems by setting (y + -0.3888888889) equal to 0.200308404 and -0.200308404.Subproblem 1
y + -0.3888888889 = 0.200308404 Simplifying y + -0.3888888889 = 0.200308404 Reorder the terms: -0.3888888889 + y = 0.200308404 Solving -0.3888888889 + y = 0.200308404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + y = 0.200308404 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + y = 0.200308404 + 0.3888888889 y = 0.200308404 + 0.3888888889 Combine like terms: 0.200308404 + 0.3888888889 = 0.5891972929 y = 0.5891972929 Simplifying y = 0.5891972929Subproblem 2
y + -0.3888888889 = -0.200308404 Simplifying y + -0.3888888889 = -0.200308404 Reorder the terms: -0.3888888889 + y = -0.200308404 Solving -0.3888888889 + y = -0.200308404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + y = -0.200308404 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + y = -0.200308404 + 0.3888888889 y = -0.200308404 + 0.3888888889 Combine like terms: -0.200308404 + 0.3888888889 = 0.1885804849 y = 0.1885804849 Simplifying y = 0.1885804849Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.5891972929, 0.1885804849}
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