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Simplifying Y2 + 4Y = 30 Reorder the terms: 4Y + Y2 = 30 Solving 4Y + Y2 = 30 Solving for variable 'Y'. Reorder the terms: -30 + 4Y + Y2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 4Y + Y2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 4Y + 30 + Y2 = 0 + 30 Reorder the terms: -30 + 30 + 4Y + Y2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 4Y + Y2 = 0 + 30 4Y + Y2 = 0 + 30 Combine like terms: 0 + 30 = 30 4Y + Y2 = 30 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 = 30 + 4 Reorder the terms: 4 + 4Y + Y2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + 4Y + Y2 = 34 Factor a perfect square on the left side: (Y + 2)(Y + 2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (Y + 2) equal to 5.830951895 and -5.830951895.Subproblem 1
Y + 2 = 5.830951895 Simplifying Y + 2 = 5.830951895 Reorder the terms: 2 + Y = 5.830951895 Solving 2 + Y = 5.830951895 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 = 5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + Y = 5.830951895 + -2 Y = 5.830951895 + -2 Combine like terms: 5.830951895 + -2 = 3.830951895 Y = 3.830951895 Simplifying Y = 3.830951895Subproblem 2
Y + 2 = -5.830951895 Simplifying Y + 2 = -5.830951895 Reorder the terms: 2 + Y = -5.830951895 Solving 2 + Y = -5.830951895 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 = -5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + Y = -5.830951895 + -2 Y = -5.830951895 + -2 Combine like terms: -5.830951895 + -2 = -7.830951895 Y = -7.830951895 Simplifying Y = -7.830951895Solution
The solution to the problem is based on the solutions from the subproblems. Y = {3.830951895, -7.830951895}
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