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Simplifying 9y2 + -8y + -50 = 0 Reorder the terms: -50 + -8y + 9y2 = 0 Solving -50 + -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'. -5.555555556 + -0.8888888889y + y2 = 0 Move the constant term to the right: Add '5.555555556' to each side of the equation. -5.555555556 + -0.8888888889y + 5.555555556 + y2 = 0 + 5.555555556 Reorder the terms: -5.555555556 + 5.555555556 + -0.8888888889y + y2 = 0 + 5.555555556 Combine like terms: -5.555555556 + 5.555555556 = 0.000000000 0.000000000 + -0.8888888889y + y2 = 0 + 5.555555556 -0.8888888889y + y2 = 0 + 5.555555556 Combine like terms: 0 + 5.555555556 = 5.555555556 -0.8888888889y + y2 = 5.555555556 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 = 5.555555556 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889y + y2 = 5.555555556 + 0.1975308642 Combine like terms: 5.555555556 + 0.1975308642 = 5.7530864202 0.1975308642 + -0.8888888889y + y2 = 5.7530864202 Factor a perfect square on the left side: (y + -0.4444444445)(y + -0.4444444445) = 5.7530864202 Calculate the square root of the right side: 2.398559238 Break this problem into two subproblems by setting (y + -0.4444444445) equal to 2.398559238 and -2.398559238.Subproblem 1
y + -0.4444444445 = 2.398559238 Simplifying y + -0.4444444445 = 2.398559238 Reorder the terms: -0.4444444445 + y = 2.398559238 Solving -0.4444444445 + y = 2.398559238 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 = 2.398559238 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + y = 2.398559238 + 0.4444444445 y = 2.398559238 + 0.4444444445 Combine like terms: 2.398559238 + 0.4444444445 = 2.8430036825 y = 2.8430036825 Simplifying y = 2.8430036825Subproblem 2
y + -0.4444444445 = -2.398559238 Simplifying y + -0.4444444445 = -2.398559238 Reorder the terms: -0.4444444445 + y = -2.398559238 Solving -0.4444444445 + y = -2.398559238 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 = -2.398559238 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + y = -2.398559238 + 0.4444444445 y = -2.398559238 + 0.4444444445 Combine like terms: -2.398559238 + 0.4444444445 = -1.9541147935 y = -1.9541147935 Simplifying y = -1.9541147935Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.8430036825, -1.9541147935}
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