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Simplifying Y2 + -18Y + 6 = 0 Reorder the terms: 6 + -18Y + Y2 = 0 Solving 6 + -18Y + Y2 = 0 Solving for variable 'Y'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -18Y + -6 + Y2 = 0 + -6 Reorder the terms: 6 + -6 + -18Y + Y2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -18Y + Y2 = 0 + -6 -18Y + Y2 = 0 + -6 Combine like terms: 0 + -6 = -6 -18Y + Y2 = -6 The Y term is -18Y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18Y + 81 + Y2 = -6 + 81 Reorder the terms: 81 + -18Y + Y2 = -6 + 81 Combine like terms: -6 + 81 = 75 81 + -18Y + Y2 = 75 Factor a perfect square on the left side: (Y + -9)(Y + -9) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (Y + -9) equal to 8.660254038 and -8.660254038.Subproblem 1
Y + -9 = 8.660254038 Simplifying Y + -9 = 8.660254038 Reorder the terms: -9 + Y = 8.660254038 Solving -9 + Y = 8.660254038 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + Y = 8.660254038 + 9 Combine like terms: -9 + 9 = 0 0 + Y = 8.660254038 + 9 Y = 8.660254038 + 9 Combine like terms: 8.660254038 + 9 = 17.660254038 Y = 17.660254038 Simplifying Y = 17.660254038Subproblem 2
Y + -9 = -8.660254038 Simplifying Y + -9 = -8.660254038 Reorder the terms: -9 + Y = -8.660254038 Solving -9 + Y = -8.660254038 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + Y = -8.660254038 + 9 Combine like terms: -9 + 9 = 0 0 + Y = -8.660254038 + 9 Y = -8.660254038 + 9 Combine like terms: -8.660254038 + 9 = 0.339745962 Y = 0.339745962 Simplifying Y = 0.339745962Solution
The solution to the problem is based on the solutions from the subproblems. Y = {17.660254038, 0.339745962}
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