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Simplifying -4 + y2 + y = 3 Reorder the terms: -4 + y + y2 = 3 Solving -4 + y + y2 = 3 Solving for variable 'y'. Reorder the terms: -4 + -3 + y + y2 = 3 + -3 Combine like terms: -4 + -3 = -7 -7 + y + y2 = 3 + -3 Combine like terms: 3 + -3 = 0 -7 + y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + y + y2 = 0 + 7 y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 y + y2 = 7 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. y + 0.25 + y2 = 7 + 0.25 Reorder the terms: 0.25 + y + y2 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 0.25 + y + y2 = 7.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (y + 0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
y + 0.5 = 2.692582404 Simplifying y + 0.5 = 2.692582404 Reorder the terms: 0.5 + y = 2.692582404 Solving 0.5 + y = 2.692582404 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 = 2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 2.692582404 + -0.5 y = 2.692582404 + -0.5 Combine like terms: 2.692582404 + -0.5 = 2.192582404 y = 2.192582404 Simplifying y = 2.192582404Subproblem 2
y + 0.5 = -2.692582404 Simplifying y + 0.5 = -2.692582404 Reorder the terms: 0.5 + y = -2.692582404 Solving 0.5 + y = -2.692582404 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 = -2.692582404 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -2.692582404 + -0.5 y = -2.692582404 + -0.5 Combine like terms: -2.692582404 + -0.5 = -3.192582404 y = -3.192582404 Simplifying y = -3.192582404Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.192582404, -3.192582404}
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