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Simplifying 9y2 + -2y + -1 = 0 Reorder the terms: -1 + -2y + 9y2 = 0 Solving -1 + -2y + 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'. -0.1111111111 + -0.2222222222y + y2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.2222222222y + 0.1111111111 + y2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.2222222222y + y2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.2222222222y + y2 = 0 + 0.1111111111 -0.2222222222y + y2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.2222222222y + y2 = 0.1111111111 The y term is -0.2222222222y. Take half its coefficient (-0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. -0.2222222222y + 0.01234567901 + y2 = 0.1111111111 + 0.01234567901 Reorder the terms: 0.01234567901 + -0.2222222222y + y2 = 0.1111111111 + 0.01234567901 Combine like terms: 0.1111111111 + 0.01234567901 = 0.12345679011 0.01234567901 + -0.2222222222y + y2 = 0.12345679011 Factor a perfect square on the left side: (y + -0.1111111111)(y + -0.1111111111) = 0.12345679011 Calculate the square root of the right side: 0.351364184 Break this problem into two subproblems by setting (y + -0.1111111111) equal to 0.351364184 and -0.351364184.Subproblem 1
y + -0.1111111111 = 0.351364184 Simplifying y + -0.1111111111 = 0.351364184 Reorder the terms: -0.1111111111 + y = 0.351364184 Solving -0.1111111111 + y = 0.351364184 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + y = 0.351364184 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + y = 0.351364184 + 0.1111111111 y = 0.351364184 + 0.1111111111 Combine like terms: 0.351364184 + 0.1111111111 = 0.4624752951 y = 0.4624752951 Simplifying y = 0.4624752951Subproblem 2
y + -0.1111111111 = -0.351364184 Simplifying y + -0.1111111111 = -0.351364184 Reorder the terms: -0.1111111111 + y = -0.351364184 Solving -0.1111111111 + y = -0.351364184 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + y = -0.351364184 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + y = -0.351364184 + 0.1111111111 y = -0.351364184 + 0.1111111111 Combine like terms: -0.351364184 + 0.1111111111 = -0.2402530729 y = -0.2402530729 Simplifying y = -0.2402530729Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.4624752951, -0.2402530729}
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