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Simplifying Y2 + -5 = -1Y2 + -2Y Reorder the terms: -5 + Y2 = -1Y2 + -2Y Reorder the terms: -5 + Y2 = -2Y + -1Y2 Solving -5 + Y2 = -2Y + -1Y2 Solving for variable 'Y'. Reorder the terms: -5 + 2Y + Y2 + Y2 = -2Y + -1Y2 + 2Y + Y2 Combine like terms: Y2 + Y2 = 2Y2 -5 + 2Y + 2Y2 = -2Y + -1Y2 + 2Y + Y2 Reorder the terms: -5 + 2Y + 2Y2 = -2Y + 2Y + -1Y2 + Y2 Combine like terms: -2Y + 2Y = 0 -5 + 2Y + 2Y2 = 0 + -1Y2 + Y2 -5 + 2Y + 2Y2 = -1Y2 + Y2 Combine like terms: -1Y2 + Y2 = 0 -5 + 2Y + 2Y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + Y + Y2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + Y + 2.5 + Y2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + Y + Y2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + Y + Y2 = 0 + 2.5 Y + Y2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 Y + Y2 = 2.5 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. + 0.25 + Y2 = 2.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + Y2 = 2.5 + 0.25 Combine like terms: 2.5 + 0.25 = 2.75 1.25 + Y2 = 2.75 Factor a perfect square on the left side: (Y + 0.5)(Y + 0.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (Y + 0.5) equal to 1.658312395 and -1.658312395.Subproblem 1
Y + 0.5 = 1.658312395 Simplifying Y + 0.5 = 1.658312395 Reorder the terms: 0.5 + Y = 1.658312395 Solving 0.5 + Y = 1.658312395 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 = 1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + Y = 1.658312395 + -0.5 Y = 1.658312395 + -0.5 Combine like terms: 1.658312395 + -0.5 = 1.158312395 Y = 1.158312395 Simplifying Y = 1.158312395Subproblem 2
Y + 0.5 = -1.658312395 Simplifying Y + 0.5 = -1.658312395 Reorder the terms: 0.5 + Y = -1.658312395 Solving 0.5 + Y = -1.658312395 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 = -1.658312395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + Y = -1.658312395 + -0.5 Y = -1.658312395 + -0.5 Combine like terms: -1.658312395 + -0.5 = -2.158312395 Y = -2.158312395 Simplifying Y = -2.158312395Solution
The solution to the problem is based on the solutions from the subproblems. Y = {1.158312395, -2.158312395}
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