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Simplifying 9y2 + 6y + -14 = 0 Reorder the terms: -14 + 6y + 9y2 = 0 Solving -14 + 6y + 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'. -1.555555556 + 0.6666666667y + y2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 0.6666666667y + 1.555555556 + y2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 0.6666666667y + y2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 0.6666666667y + y2 = 0 + 1.555555556 0.6666666667y + y2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 0.6666666667y + y2 = 1.555555556 The y term is 0.6666666667y. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667y + 0.1111111112 + y2 = 1.555555556 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667y + y2 = 1.555555556 + 0.1111111112 Combine like terms: 1.555555556 + 0.1111111112 = 1.6666666672 0.1111111112 + 0.6666666667y + y2 = 1.6666666672 Factor a perfect square on the left side: (y + 0.3333333334)(y + 0.3333333334) = 1.6666666672 Calculate the square root of the right side: 1.290994449 Break this problem into two subproblems by setting (y + 0.3333333334) equal to 1.290994449 and -1.290994449.Subproblem 1
y + 0.3333333334 = 1.290994449 Simplifying y + 0.3333333334 = 1.290994449 Reorder the terms: 0.3333333334 + y = 1.290994449 Solving 0.3333333334 + y = 1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + y = 1.290994449 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + y = 1.290994449 + -0.3333333334 y = 1.290994449 + -0.3333333334 Combine like terms: 1.290994449 + -0.3333333334 = 0.9576611156 y = 0.9576611156 Simplifying y = 0.9576611156Subproblem 2
y + 0.3333333334 = -1.290994449 Simplifying y + 0.3333333334 = -1.290994449 Reorder the terms: 0.3333333334 + y = -1.290994449 Solving 0.3333333334 + y = -1.290994449 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + y = -1.290994449 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + y = -1.290994449 + -0.3333333334 y = -1.290994449 + -0.3333333334 Combine like terms: -1.290994449 + -0.3333333334 = -1.6243277824 y = -1.6243277824 Simplifying y = -1.6243277824Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.9576611156, -1.6243277824}
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