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Simplifying Y2 + -6Y = -3 Reorder the terms: -6Y + Y2 = -3 Solving -6Y + Y2 = -3 Solving for variable 'Y'. Reorder the terms: 3 + -6Y + Y2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + -6Y + Y2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6Y + -3 + Y2 = 0 + -3 Reorder the terms: 3 + -3 + -6Y + Y2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6Y + Y2 = 0 + -3 -6Y + Y2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6Y + Y2 = -3 The Y term is -6Y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6Y + 9 + Y2 = -3 + 9 Reorder the terms: 9 + -6Y + Y2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6Y + Y2 = 6 Factor a perfect square on the left side: (Y + -3)(Y + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (Y + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
Y + -3 = 2.449489743 Simplifying Y + -3 = 2.449489743 Reorder the terms: -3 + Y = 2.449489743 Solving -3 + Y = 2.449489743 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + Y = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + Y = 2.449489743 + 3 Y = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 Y = 5.449489743 Simplifying Y = 5.449489743Subproblem 2
Y + -3 = -2.449489743 Simplifying Y + -3 = -2.449489743 Reorder the terms: -3 + Y = -2.449489743 Solving -3 + Y = -2.449489743 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + Y = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + Y = -2.449489743 + 3 Y = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 Y = 0.550510257 Simplifying Y = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. Y = {5.449489743, 0.550510257}
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