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Simplifying Y2 + 4Y + -400 = 0 Reorder the terms: -400 + 4Y + Y2 = 0 Solving -400 + 4Y + Y2 = 0 Solving for variable 'Y'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 4Y + 400 + Y2 = 0 + 400 Reorder the terms: -400 + 400 + 4Y + Y2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 4Y + Y2 = 0 + 400 4Y + Y2 = 0 + 400 Combine like terms: 0 + 400 = 400 4Y + Y2 = 400 The Y term is 4Y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4Y + 4 + Y2 = 400 + 4 Reorder the terms: 4 + 4Y + Y2 = 400 + 4 Combine like terms: 400 + 4 = 404 4 + 4Y + Y2 = 404 Factor a perfect square on the left side: (Y + 2)(Y + 2) = 404 Calculate the square root of the right side: 20.099751242 Break this problem into two subproblems by setting (Y + 2) equal to 20.099751242 and -20.099751242.Subproblem 1
Y + 2 = 20.099751242 Simplifying Y + 2 = 20.099751242 Reorder the terms: 2 + Y = 20.099751242 Solving 2 + Y = 20.099751242 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + Y = 20.099751242 + -2 Combine like terms: 2 + -2 = 0 0 + Y = 20.099751242 + -2 Y = 20.099751242 + -2 Combine like terms: 20.099751242 + -2 = 18.099751242 Y = 18.099751242 Simplifying Y = 18.099751242Subproblem 2
Y + 2 = -20.099751242 Simplifying Y + 2 = -20.099751242 Reorder the terms: 2 + Y = -20.099751242 Solving 2 + Y = -20.099751242 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + Y = -20.099751242 + -2 Combine like terms: 2 + -2 = 0 0 + Y = -20.099751242 + -2 Y = -20.099751242 + -2 Combine like terms: -20.099751242 + -2 = -22.099751242 Y = -22.099751242 Simplifying Y = -22.099751242Solution
The solution to the problem is based on the solutions from the subproblems. Y = {18.099751242, -22.099751242}
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