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Simplifying 9y2 + 18y + 2 = 0 Reorder the terms: 2 + 18y + 9y2 = 0 Solving 2 + 18y + 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'. 0.2222222222 + 2y + y2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 2y + -0.2222222222 + y2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 2y + y2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 2y + y2 = 0 + -0.2222222222 2y + y2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 2y + y2 = -0.2222222222 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = -0.2222222222 + 1 Reorder the terms: 1 + 2y + y2 = -0.2222222222 + 1 Combine like terms: -0.2222222222 + 1 = 0.7777777778 1 + 2y + y2 = 0.7777777778 Factor a perfect square on the left side: (y + 1)(y + 1) = 0.7777777778 Calculate the square root of the right side: 0.881917104 Break this problem into two subproblems by setting (y + 1) equal to 0.881917104 and -0.881917104.Subproblem 1
y + 1 = 0.881917104 Simplifying y + 1 = 0.881917104 Reorder the terms: 1 + y = 0.881917104 Solving 1 + y = 0.881917104 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 0.881917104 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0.881917104 + -1 y = 0.881917104 + -1 Combine like terms: 0.881917104 + -1 = -0.118082896 y = -0.118082896 Simplifying y = -0.118082896Subproblem 2
y + 1 = -0.881917104 Simplifying y + 1 = -0.881917104 Reorder the terms: 1 + y = -0.881917104 Solving 1 + y = -0.881917104 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -0.881917104 + -1 Combine like terms: 1 + -1 = 0 0 + y = -0.881917104 + -1 y = -0.881917104 + -1 Combine like terms: -0.881917104 + -1 = -1.881917104 y = -1.881917104 Simplifying y = -1.881917104Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.118082896, -1.881917104}
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