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Simplifying (9y2 + -18y + -4) + -1(-13y2 + 3y + 7) = 0 Reorder the terms: (-4 + -18y + 9y2) + -1(-13y2 + 3y + 7) = 0 Remove parenthesis around (-4 + -18y + 9y2) -4 + -18y + 9y2 + -1(-13y2 + 3y + 7) = 0 Reorder the terms: -4 + -18y + 9y2 + -1(7 + 3y + -13y2) = 0 -4 + -18y + 9y2 + (7 * -1 + 3y * -1 + -13y2 * -1) = 0 -4 + -18y + 9y2 + (-7 + -3y + 13y2) = 0 Reorder the terms: -4 + -7 + -18y + -3y + 9y2 + 13y2 = 0 Combine like terms: -4 + -7 = -11 -11 + -18y + -3y + 9y2 + 13y2 = 0 Combine like terms: -18y + -3y = -21y -11 + -21y + 9y2 + 13y2 = 0 Combine like terms: 9y2 + 13y2 = 22y2 -11 + -21y + 22y2 = 0 Solving -11 + -21y + 22y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. -0.5 + -0.9545454545y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.9545454545y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.9545454545y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.9545454545y + y2 = 0 + 0.5 -0.9545454545y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.9545454545y + y2 = 0.5 The y term is -0.9545454545y. Take half its coefficient (-0.4772727273). Square it (0.2277892562) and add it to both sides. Add '0.2277892562' to each side of the equation. -0.9545454545y + 0.2277892562 + y2 = 0.5 + 0.2277892562 Reorder the terms: 0.2277892562 + -0.9545454545y + y2 = 0.5 + 0.2277892562 Combine like terms: 0.5 + 0.2277892562 = 0.7277892562 0.2277892562 + -0.9545454545y + y2 = 0.7277892562 Factor a perfect square on the left side: (y + -0.4772727273)(y + -0.4772727273) = 0.7277892562 Calculate the square root of the right side: 0.853105654 Break this problem into two subproblems by setting (y + -0.4772727273) equal to 0.853105654 and -0.853105654.Subproblem 1
y + -0.4772727273 = 0.853105654 Simplifying y + -0.4772727273 = 0.853105654 Reorder the terms: -0.4772727273 + y = 0.853105654 Solving -0.4772727273 + y = 0.853105654 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4772727273' to each side of the equation. -0.4772727273 + 0.4772727273 + y = 0.853105654 + 0.4772727273 Combine like terms: -0.4772727273 + 0.4772727273 = 0.0000000000 0.0000000000 + y = 0.853105654 + 0.4772727273 y = 0.853105654 + 0.4772727273 Combine like terms: 0.853105654 + 0.4772727273 = 1.3303783813 y = 1.3303783813 Simplifying y = 1.3303783813Subproblem 2
y + -0.4772727273 = -0.853105654 Simplifying y + -0.4772727273 = -0.853105654 Reorder the terms: -0.4772727273 + y = -0.853105654 Solving -0.4772727273 + y = -0.853105654 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4772727273' to each side of the equation. -0.4772727273 + 0.4772727273 + y = -0.853105654 + 0.4772727273 Combine like terms: -0.4772727273 + 0.4772727273 = 0.0000000000 0.0000000000 + y = -0.853105654 + 0.4772727273 y = -0.853105654 + 0.4772727273 Combine like terms: -0.853105654 + 0.4772727273 = -0.3758329267 y = -0.3758329267 Simplifying y = -0.3758329267Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.3303783813, -0.3758329267}
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