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Simplifying y2 + 3y + -5 = 0 Reorder the terms: -5 + 3y + y2 = 0 Solving -5 + 3y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 3y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + 3y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3y + y2 = 0 + 5 3y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 3y + y2 = 5 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = 5 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 5 + 2.25 Combine like terms: 5 + 2.25 = 7.25 2.25 + 3y + y2 = 7.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (y + 1.5) equal to 2.692582404 and -2.692582404.Subproblem 1
y + 1.5 = 2.692582404 Simplifying y + 1.5 = 2.692582404 Reorder the terms: 1.5 + y = 2.692582404 Solving 1.5 + y = 2.692582404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = 2.692582404 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 2.692582404 + -1.5 y = 2.692582404 + -1.5 Combine like terms: 2.692582404 + -1.5 = 1.192582404 y = 1.192582404 Simplifying y = 1.192582404Subproblem 2
y + 1.5 = -2.692582404 Simplifying y + 1.5 = -2.692582404 Reorder the terms: 1.5 + y = -2.692582404 Solving 1.5 + y = -2.692582404 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + y = -2.692582404 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -2.692582404 + -1.5 y = -2.692582404 + -1.5 Combine like terms: -2.692582404 + -1.5 = -4.192582404 y = -4.192582404 Simplifying y = -4.192582404Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.192582404, -4.192582404}
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