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Simplifying 2y2 + 30y + -3y2 + 4y + -14 + -1y = 0 Reorder the terms: -14 + 30y + 4y + -1y + 2y2 + -3y2 = 0 Combine like terms: 30y + 4y = 34y -14 + 34y + -1y + 2y2 + -3y2 = 0 Combine like terms: 34y + -1y = 33y -14 + 33y + 2y2 + -3y2 = 0 Combine like terms: 2y2 + -3y2 = -1y2 -14 + 33y + -1y2 = 0 Solving -14 + 33y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 14 + -33y + y2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -33y + -14 + y2 = 0 + -14 Reorder the terms: 14 + -14 + -33y + y2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -33y + y2 = 0 + -14 -33y + y2 = 0 + -14 Combine like terms: 0 + -14 = -14 -33y + y2 = -14 The y term is -33y. Take half its coefficient (-16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. -33y + 272.25 + y2 = -14 + 272.25 Reorder the terms: 272.25 + -33y + y2 = -14 + 272.25 Combine like terms: -14 + 272.25 = 258.25 272.25 + -33y + y2 = 258.25 Factor a perfect square on the left side: (y + -16.5)(y + -16.5) = 258.25 Calculate the square root of the right side: 16.07015868 Break this problem into two subproblems by setting (y + -16.5) equal to 16.07015868 and -16.07015868.Subproblem 1
y + -16.5 = 16.07015868 Simplifying y + -16.5 = 16.07015868 Reorder the terms: -16.5 + y = 16.07015868 Solving -16.5 + y = 16.07015868 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + y = 16.07015868 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + y = 16.07015868 + 16.5 y = 16.07015868 + 16.5 Combine like terms: 16.07015868 + 16.5 = 32.57015868 y = 32.57015868 Simplifying y = 32.57015868Subproblem 2
y + -16.5 = -16.07015868 Simplifying y + -16.5 = -16.07015868 Reorder the terms: -16.5 + y = -16.07015868 Solving -16.5 + y = -16.07015868 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '16.5' to each side of the equation. -16.5 + 16.5 + y = -16.07015868 + 16.5 Combine like terms: -16.5 + 16.5 = 0.0 0.0 + y = -16.07015868 + 16.5 y = -16.07015868 + 16.5 Combine like terms: -16.07015868 + 16.5 = 0.42984132 y = 0.42984132 Simplifying y = 0.42984132Solution
The solution to the problem is based on the solutions from the subproblems. y = {32.57015868, 0.42984132}
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