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Simplifying 9y2 + -8y + -12 = 0 Reorder the terms: -12 + -8y + 9y2 = 0 Solving -12 + -8y + 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'. -1.333333333 + -0.8888888889y + y2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.8888888889y + 1.333333333 + y2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.8888888889y + y2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.8888888889y + y2 = 0 + 1.333333333 -0.8888888889y + y2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.8888888889y + y2 = 1.333333333 The y term is -0.8888888889y. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889y + 0.1975308642 + y2 = 1.333333333 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889y + y2 = 1.333333333 + 0.1975308642 Combine like terms: 1.333333333 + 0.1975308642 = 1.5308641972 0.1975308642 + -0.8888888889y + y2 = 1.5308641972 Factor a perfect square on the left side: (y + -0.4444444445)(y + -0.4444444445) = 1.5308641972 Calculate the square root of the right side: 1.237280969 Break this problem into two subproblems by setting (y + -0.4444444445) equal to 1.237280969 and -1.237280969.Subproblem 1
y + -0.4444444445 = 1.237280969 Simplifying y + -0.4444444445 = 1.237280969 Reorder the terms: -0.4444444445 + y = 1.237280969 Solving -0.4444444445 + y = 1.237280969 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + y = 1.237280969 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + y = 1.237280969 + 0.4444444445 y = 1.237280969 + 0.4444444445 Combine like terms: 1.237280969 + 0.4444444445 = 1.6817254135 y = 1.6817254135 Simplifying y = 1.6817254135Subproblem 2
y + -0.4444444445 = -1.237280969 Simplifying y + -0.4444444445 = -1.237280969 Reorder the terms: -0.4444444445 + y = -1.237280969 Solving -0.4444444445 + y = -1.237280969 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + y = -1.237280969 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + y = -1.237280969 + 0.4444444445 y = -1.237280969 + 0.4444444445 Combine like terms: -1.237280969 + 0.4444444445 = -0.7928365245 y = -0.7928365245 Simplifying y = -0.7928365245Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.6817254135, -0.7928365245}
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