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Simplifying [(-4y2 + 7y + -9) + -1(8y2 + 5y + -6)] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 Reorder the terms: [(-9 + 7y + -4y2) + -1(8y2 + 5y + -6)] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 Remove parenthesis around (-9 + 7y + -4y2) [-9 + 7y + -4y2 + -1(8y2 + 5y + -6)] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 Reorder the terms: [-9 + 7y + -4y2 + -1(-6 + 5y + 8y2)] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 [-9 + 7y + -4y2 + (-6 * -1 + 5y * -1 + 8y2 * -1)] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 [-9 + 7y + -4y2 + (6 + -5y + -8y2)] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 Reorder the terms: [-9 + 6 + 7y + -5y + -4y2 + -8y2] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 Combine like terms: -9 + 6 = -3 [-3 + 7y + -5y + -4y2 + -8y2] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 Combine like terms: 7y + -5y = 2y [-3 + 2y + -4y2 + -8y2] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 Combine like terms: -4y2 + -8y2 = -12y2 [-3 + 2y + -12y2] + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 Remove brackets around [-3 + 2y + -12y2] -3 + 2y + -12y2 + -1[(-3y2 + -5y + 4) + (-10y2 + -3y + 7)] = 0 Reorder the terms: -3 + 2y + -12y2 + -1[(4 + -5y + -3y2) + (-10y2 + -3y + 7)] = 0 Remove parenthesis around (4 + -5y + -3y2) -3 + 2y + -12y2 + -1[4 + -5y + -3y2 + (-10y2 + -3y + 7)] = 0 Reorder the terms: -3 + 2y + -12y2 + -1[4 + -5y + -3y2 + (7 + -3y + -10y2)] = 0 Remove parenthesis around (7 + -3y + -10y2) -3 + 2y + -12y2 + -1[4 + -5y + -3y2 + 7 + -3y + -10y2] = 0 Reorder the terms: -3 + 2y + -12y2 + -1[4 + 7 + -5y + -3y + -3y2 + -10y2] = 0 Combine like terms: 4 + 7 = 11 -3 + 2y + -12y2 + -1[11 + -5y + -3y + -3y2 + -10y2] = 0 Combine like terms: -5y + -3y = -8y -3 + 2y + -12y2 + -1[11 + -8y + -3y2 + -10y2] = 0 Combine like terms: -3y2 + -10y2 = -13y2 -3 + 2y + -12y2 + -1[11 + -8y + -13y2] = 0 -3 + 2y + -12y2 + [11 * -1 + -8y * -1 + -13y2 * -1] = 0 -3 + 2y + -12y2 + [-11 + 8y + 13y2] = 0 Reorder the terms: -3 + -11 + 2y + 8y + -12y2 + 13y2 = 0 Combine like terms: -3 + -11 = -14 -14 + 2y + 8y + -12y2 + 13y2 = 0 Combine like terms: 2y + 8y = 10y -14 + 10y + -12y2 + 13y2 = 0 Combine like terms: -12y2 + 13y2 = 1y2 -14 + 10y + 1y2 = 0 Solving -14 + 10y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 10y + 14 + y2 = 0 + 14 Reorder the terms: -14 + 14 + 10y + y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 10y + y2 = 0 + 14 10y + y2 = 0 + 14 Combine like terms: 0 + 14 = 14 10y + y2 = 14 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 = 14 + 25 Reorder the terms: 25 + 10y + y2 = 14 + 25 Combine like terms: 14 + 25 = 39 25 + 10y + y2 = 39 Factor a perfect square on the left side: (y + 5)(y + 5) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (y + 5) equal to 6.244997998 and -6.244997998.Subproblem 1
y + 5 = 6.244997998 Simplifying y + 5 = 6.244997998 Reorder the terms: 5 + y = 6.244997998 Solving 5 + y = 6.244997998 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 = 6.244997998 + -5 Combine like terms: 5 + -5 = 0 0 + y = 6.244997998 + -5 y = 6.244997998 + -5 Combine like terms: 6.244997998 + -5 = 1.244997998 y = 1.244997998 Simplifying y = 1.244997998Subproblem 2
y + 5 = -6.244997998 Simplifying y + 5 = -6.244997998 Reorder the terms: 5 + y = -6.244997998 Solving 5 + y = -6.244997998 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 = -6.244997998 + -5 Combine like terms: 5 + -5 = 0 0 + y = -6.244997998 + -5 y = -6.244997998 + -5 Combine like terms: -6.244997998 + -5 = -11.244997998 y = -11.244997998 Simplifying y = -11.244997998Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.244997998, -11.244997998}
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