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Simplifying 15y2 + y + -81 = 0 Reorder the terms: -81 + y + 15y2 = 0 Solving -81 + y + 15y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -5.4 + 0.06666666667y + y2 = 0 Move the constant term to the right: Add '5.4' to each side of the equation. -5.4 + 0.06666666667y + 5.4 + y2 = 0 + 5.4 Reorder the terms: -5.4 + 5.4 + 0.06666666667y + y2 = 0 + 5.4 Combine like terms: -5.4 + 5.4 = 0.0 0.0 + 0.06666666667y + y2 = 0 + 5.4 0.06666666667y + y2 = 0 + 5.4 Combine like terms: 0 + 5.4 = 5.4 0.06666666667y + y2 = 5.4 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.06666666667y + 0.25 + y2 = 5.4 + 0.25 Reorder the terms: 0.25 + 0.06666666667y + y2 = 5.4 + 0.25 Combine like terms: 5.4 + 0.25 = 5.65 0.25 + 0.06666666667y + y2 = 5.65 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 5.65 Calculate the square root of the right side: 2.376972865 Break this problem into two subproblems by setting (y + 0.5) equal to 2.376972865 and -2.376972865.Subproblem 1
y + 0.5 = 2.376972865 Simplifying y + 0.5 = 2.376972865 Reorder the terms: 0.5 + y = 2.376972865 Solving 0.5 + y = 2.376972865 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 2.376972865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 2.376972865 + -0.5 y = 2.376972865 + -0.5 Combine like terms: 2.376972865 + -0.5 = 1.876972865 y = 1.876972865 Simplifying y = 1.876972865Subproblem 2
y + 0.5 = -2.376972865 Simplifying y + 0.5 = -2.376972865 Reorder the terms: 0.5 + y = -2.376972865 Solving 0.5 + y = -2.376972865 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -2.376972865 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -2.376972865 + -0.5 y = -2.376972865 + -0.5 Combine like terms: -2.376972865 + -0.5 = -2.876972865 y = -2.876972865 Simplifying y = -2.876972865Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.876972865, -2.876972865}
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