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Simplifying (4y + -5 + -1y2) + (6y + 2y2 + -2) = 0 Reorder the terms: (-5 + 4y + -1y2) + (6y + 2y2 + -2) = 0 Remove parenthesis around (-5 + 4y + -1y2) -5 + 4y + -1y2 + (6y + 2y2 + -2) = 0 Reorder the terms: -5 + 4y + -1y2 + (-2 + 6y + 2y2) = 0 Remove parenthesis around (-2 + 6y + 2y2) -5 + 4y + -1y2 + -2 + 6y + 2y2 = 0 Reorder the terms: -5 + -2 + 4y + 6y + -1y2 + 2y2 = 0 Combine like terms: -5 + -2 = -7 -7 + 4y + 6y + -1y2 + 2y2 = 0 Combine like terms: 4y + 6y = 10y -7 + 10y + -1y2 + 2y2 = 0 Combine like terms: -1y2 + 2y2 = 1y2 -7 + 10y + 1y2 = 0 Solving -7 + 10y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 10y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + 10y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 10y + y2 = 0 + 7 10y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 10y + y2 = 7 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = 7 + 25 Reorder the terms: 25 + 10y + y2 = 7 + 25 Combine like terms: 7 + 25 = 32 25 + 10y + y2 = 32 Factor a perfect square on the left side: (y + 5)(y + 5) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (y + 5) equal to 5.656854249 and -5.656854249.Subproblem 1
y + 5 = 5.656854249 Simplifying y + 5 = 5.656854249 Reorder the terms: 5 + y = 5.656854249 Solving 5 + y = 5.656854249 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + y = 5.656854249 + -5 y = 5.656854249 + -5 Combine like terms: 5.656854249 + -5 = 0.656854249 y = 0.656854249 Simplifying y = 0.656854249Subproblem 2
y + 5 = -5.656854249 Simplifying y + 5 = -5.656854249 Reorder the terms: 5 + y = -5.656854249 Solving 5 + y = -5.656854249 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -5.656854249 + -5 Combine like terms: 5 + -5 = 0 0 + y = -5.656854249 + -5 y = -5.656854249 + -5 Combine like terms: -5.656854249 + -5 = -10.656854249 y = -10.656854249 Simplifying y = -10.656854249Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.656854249, -10.656854249}
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