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Simplifying Y2 + -1Y + -45 = 0 Reorder the terms: -45 + -1Y + Y2 = 0 Solving -45 + -1Y + Y2 = 0 Solving for variable 'Y'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -1Y + 45 + Y2 = 0 + 45 Reorder the terms: -45 + 45 + -1Y + Y2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -1Y + Y2 = 0 + 45 -1Y + Y2 = 0 + 45 Combine like terms: 0 + 45 = 45 -1Y + Y2 = 45 The Y term is -1Y. 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. -1Y + 0.25 + Y2 = 45 + 0.25 Reorder the terms: 0.25 + -1Y + Y2 = 45 + 0.25 Combine like terms: 45 + 0.25 = 45.25 0.25 + -1Y + Y2 = 45.25 Factor a perfect square on the left side: (Y + -0.5)(Y + -0.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (Y + -0.5) equal to 6.726812024 and -6.726812024.Subproblem 1
Y + -0.5 = 6.726812024 Simplifying Y + -0.5 = 6.726812024 Reorder the terms: -0.5 + Y = 6.726812024 Solving -0.5 + Y = 6.726812024 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 = 6.726812024 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + Y = 6.726812024 + 0.5 Y = 6.726812024 + 0.5 Combine like terms: 6.726812024 + 0.5 = 7.226812024 Y = 7.226812024 Simplifying Y = 7.226812024Subproblem 2
Y + -0.5 = -6.726812024 Simplifying Y + -0.5 = -6.726812024 Reorder the terms: -0.5 + Y = -6.726812024 Solving -0.5 + Y = -6.726812024 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 = -6.726812024 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + Y = -6.726812024 + 0.5 Y = -6.726812024 + 0.5 Combine like terms: -6.726812024 + 0.5 = -6.226812024 Y = -6.226812024 Simplifying Y = -6.226812024Solution
The solution to the problem is based on the solutions from the subproblems. Y = {7.226812024, -6.226812024}
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