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Simplifying 40y2 + -217y + -444 = 0 Reorder the terms: -444 + -217y + 40y2 = 0 Solving -444 + -217y + 40y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -11.1 + -5.425y + y2 = 0 Move the constant term to the right: Add '11.1' to each side of the equation. -11.1 + -5.425y + 11.1 + y2 = 0 + 11.1 Reorder the terms: -11.1 + 11.1 + -5.425y + y2 = 0 + 11.1 Combine like terms: -11.1 + 11.1 = 0.0 0.0 + -5.425y + y2 = 0 + 11.1 -5.425y + y2 = 0 + 11.1 Combine like terms: 0 + 11.1 = 11.1 -5.425y + y2 = 11.1 The y term is -5.425y. Take half its coefficient (-2.7125). Square it (7.35765625) and add it to both sides. Add '7.35765625' to each side of the equation. -5.425y + 7.35765625 + y2 = 11.1 + 7.35765625 Reorder the terms: 7.35765625 + -5.425y + y2 = 11.1 + 7.35765625 Combine like terms: 11.1 + 7.35765625 = 18.45765625 7.35765625 + -5.425y + y2 = 18.45765625 Factor a perfect square on the left side: (y + -2.7125)(y + -2.7125) = 18.45765625 Calculate the square root of the right side: 4.296237453 Break this problem into two subproblems by setting (y + -2.7125) equal to 4.296237453 and -4.296237453.Subproblem 1
y + -2.7125 = 4.296237453 Simplifying y + -2.7125 = 4.296237453 Reorder the terms: -2.7125 + y = 4.296237453 Solving -2.7125 + y = 4.296237453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.7125' to each side of the equation. -2.7125 + 2.7125 + y = 4.296237453 + 2.7125 Combine like terms: -2.7125 + 2.7125 = 0.0000 0.0000 + y = 4.296237453 + 2.7125 y = 4.296237453 + 2.7125 Combine like terms: 4.296237453 + 2.7125 = 7.008737453 y = 7.008737453 Simplifying y = 7.008737453Subproblem 2
y + -2.7125 = -4.296237453 Simplifying y + -2.7125 = -4.296237453 Reorder the terms: -2.7125 + y = -4.296237453 Solving -2.7125 + y = -4.296237453 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.7125' to each side of the equation. -2.7125 + 2.7125 + y = -4.296237453 + 2.7125 Combine like terms: -2.7125 + 2.7125 = 0.0000 0.0000 + y = -4.296237453 + 2.7125 y = -4.296237453 + 2.7125 Combine like terms: -4.296237453 + 2.7125 = -1.583737453 y = -1.583737453 Simplifying y = -1.583737453Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.008737453, -1.583737453}
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