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Simplifying (4y2 + 9y + -9) + -1(-2y + 2) = 0 Reorder the terms: (-9 + 9y + 4y2) + -1(-2y + 2) = 0 Remove parenthesis around (-9 + 9y + 4y2) -9 + 9y + 4y2 + -1(-2y + 2) = 0 Reorder the terms: -9 + 9y + 4y2 + -1(2 + -2y) = 0 -9 + 9y + 4y2 + (2 * -1 + -2y * -1) = 0 -9 + 9y + 4y2 + (-2 + 2y) = 0 Reorder the terms: -9 + -2 + 9y + 2y + 4y2 = 0 Combine like terms: -9 + -2 = -11 -11 + 9y + 2y + 4y2 = 0 Combine like terms: 9y + 2y = 11y -11 + 11y + 4y2 = 0 Solving -11 + 11y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + 2.75y + y2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 2.75y + 2.75 + y2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 2.75y + y2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 2.75y + y2 = 0 + 2.75 2.75y + y2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 2.75y + y2 = 2.75 The y term is 2.75y. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75y + 1.890625 + y2 = 2.75 + 1.890625 Reorder the terms: 1.890625 + 2.75y + y2 = 2.75 + 1.890625 Combine like terms: 2.75 + 1.890625 = 4.640625 1.890625 + 2.75y + y2 = 4.640625 Factor a perfect square on the left side: (y + 1.375)(y + 1.375) = 4.640625 Calculate the square root of the right side: 2.154210992 Break this problem into two subproblems by setting (y + 1.375) equal to 2.154210992 and -2.154210992.Subproblem 1
y + 1.375 = 2.154210992 Simplifying y + 1.375 = 2.154210992 Reorder the terms: 1.375 + y = 2.154210992 Solving 1.375 + y = 2.154210992 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + y = 2.154210992 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + y = 2.154210992 + -1.375 y = 2.154210992 + -1.375 Combine like terms: 2.154210992 + -1.375 = 0.779210992 y = 0.779210992 Simplifying y = 0.779210992Subproblem 2
y + 1.375 = -2.154210992 Simplifying y + 1.375 = -2.154210992 Reorder the terms: 1.375 + y = -2.154210992 Solving 1.375 + y = -2.154210992 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + y = -2.154210992 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + y = -2.154210992 + -1.375 y = -2.154210992 + -1.375 Combine like terms: -2.154210992 + -1.375 = -3.529210992 y = -3.529210992 Simplifying y = -3.529210992Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.779210992, -3.529210992}
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