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Simplifying 2y2 + -7y + 10 + -11y2 + -7y + 1 = 0 Reorder the terms: 10 + 1 + -7y + -7y + 2y2 + -11y2 = 0 Combine like terms: 10 + 1 = 11 11 + -7y + -7y + 2y2 + -11y2 = 0 Combine like terms: -7y + -7y = -14y 11 + -14y + 2y2 + -11y2 = 0 Combine like terms: 2y2 + -11y2 = -9y2 11 + -14y + -9y2 = 0 Solving 11 + -14y + -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'. -1.222222222 + 1.555555556y + y2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + 1.555555556y + 1.222222222 + y2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + 1.555555556y + y2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + 1.555555556y + y2 = 0 + 1.222222222 1.555555556y + y2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 1.555555556y + y2 = 1.222222222 The y term is 1.555555556y. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556y + 0.6049382720 + y2 = 1.222222222 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556y + y2 = 1.222222222 + 0.6049382720 Combine like terms: 1.222222222 + 0.6049382720 = 1.827160494 0.6049382720 + 1.555555556y + y2 = 1.827160494 Factor a perfect square on the left side: (y + 0.777777778)(y + 0.777777778) = 1.827160494 Calculate the square root of the right side: 1.351725007 Break this problem into two subproblems by setting (y + 0.777777778) equal to 1.351725007 and -1.351725007.Subproblem 1
y + 0.777777778 = 1.351725007 Simplifying y + 0.777777778 = 1.351725007 Reorder the terms: 0.777777778 + y = 1.351725007 Solving 0.777777778 + y = 1.351725007 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + y = 1.351725007 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + y = 1.351725007 + -0.777777778 y = 1.351725007 + -0.777777778 Combine like terms: 1.351725007 + -0.777777778 = 0.573947229 y = 0.573947229 Simplifying y = 0.573947229Subproblem 2
y + 0.777777778 = -1.351725007 Simplifying y + 0.777777778 = -1.351725007 Reorder the terms: 0.777777778 + y = -1.351725007 Solving 0.777777778 + y = -1.351725007 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + y = -1.351725007 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + y = -1.351725007 + -0.777777778 y = -1.351725007 + -0.777777778 Combine like terms: -1.351725007 + -0.777777778 = -2.129502785 y = -2.129502785 Simplifying y = -2.129502785Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.573947229, -2.129502785}
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