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Simplifying (9y2 + 4y + -2) + -1(-7y + 8) = 0 Reorder the terms: (-2 + 4y + 9y2) + -1(-7y + 8) = 0 Remove parenthesis around (-2 + 4y + 9y2) -2 + 4y + 9y2 + -1(-7y + 8) = 0 Reorder the terms: -2 + 4y + 9y2 + -1(8 + -7y) = 0 -2 + 4y + 9y2 + (8 * -1 + -7y * -1) = 0 -2 + 4y + 9y2 + (-8 + 7y) = 0 Reorder the terms: -2 + -8 + 4y + 7y + 9y2 = 0 Combine like terms: -2 + -8 = -10 -10 + 4y + 7y + 9y2 = 0 Combine like terms: 4y + 7y = 11y -10 + 11y + 9y2 = 0 Solving -10 + 11y + 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'. -1.111111111 + 1.222222222y + y2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + 1.222222222y + 1.111111111 + y2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + 1.222222222y + y2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + 1.222222222y + y2 = 0 + 1.111111111 1.222222222y + y2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 1.222222222y + y2 = 1.111111111 The y term is 1.222222222y. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222y + 0.3734567900 + y2 = 1.111111111 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222y + y2 = 1.111111111 + 0.3734567900 Combine like terms: 1.111111111 + 0.3734567900 = 1.484567901 0.3734567900 + 1.222222222y + y2 = 1.484567901 Factor a perfect square on the left side: (y + 0.611111111)(y + 0.611111111) = 1.484567901 Calculate the square root of the right side: 1.218428455 Break this problem into two subproblems by setting (y + 0.611111111) equal to 1.218428455 and -1.218428455.Subproblem 1
y + 0.611111111 = 1.218428455 Simplifying y + 0.611111111 = 1.218428455 Reorder the terms: 0.611111111 + y = 1.218428455 Solving 0.611111111 + y = 1.218428455 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + y = 1.218428455 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + y = 1.218428455 + -0.611111111 y = 1.218428455 + -0.611111111 Combine like terms: 1.218428455 + -0.611111111 = 0.607317344 y = 0.607317344 Simplifying y = 0.607317344Subproblem 2
y + 0.611111111 = -1.218428455 Simplifying y + 0.611111111 = -1.218428455 Reorder the terms: 0.611111111 + y = -1.218428455 Solving 0.611111111 + y = -1.218428455 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + y = -1.218428455 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + y = -1.218428455 + -0.611111111 y = -1.218428455 + -0.611111111 Combine like terms: -1.218428455 + -0.611111111 = -1.829539566 y = -1.829539566 Simplifying y = -1.829539566Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.607317344, -1.829539566}
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