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Simplifying Y2 + 3Y = 6 Reorder the terms: 3Y + Y2 = 6 Solving 3Y + Y2 = 6 Solving for variable 'Y'. Reorder the terms: -6 + 3Y + Y2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 3Y + Y2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 3Y + 6 + Y2 = 0 + 6 Reorder the terms: -6 + 6 + 3Y + Y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3Y + Y2 = 0 + 6 3Y + Y2 = 0 + 6 Combine like terms: 0 + 6 = 6 3Y + Y2 = 6 The Y term is 3Y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3Y + 2.25 + Y2 = 6 + 2.25 Reorder the terms: 2.25 + 3Y + Y2 = 6 + 2.25 Combine like terms: 6 + 2.25 = 8.25 2.25 + 3Y + Y2 = 8.25 Factor a perfect square on the left side: (Y + 1.5)(Y + 1.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (Y + 1.5) equal to 2.872281323 and -2.872281323.Subproblem 1
Y + 1.5 = 2.872281323 Simplifying Y + 1.5 = 2.872281323 Reorder the terms: 1.5 + Y = 2.872281323 Solving 1.5 + Y = 2.872281323 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + Y = 2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + Y = 2.872281323 + -1.5 Y = 2.872281323 + -1.5 Combine like terms: 2.872281323 + -1.5 = 1.372281323 Y = 1.372281323 Simplifying Y = 1.372281323Subproblem 2
Y + 1.5 = -2.872281323 Simplifying Y + 1.5 = -2.872281323 Reorder the terms: 1.5 + Y = -2.872281323 Solving 1.5 + Y = -2.872281323 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + Y = -2.872281323 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + Y = -2.872281323 + -1.5 Y = -2.872281323 + -1.5 Combine like terms: -2.872281323 + -1.5 = -4.372281323 Y = -4.372281323 Simplifying Y = -4.372281323Solution
The solution to the problem is based on the solutions from the subproblems. Y = {1.372281323, -4.372281323}
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