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Simplifying Y2 + -3Y = 15 Reorder the terms: -3Y + Y2 = 15 Solving -3Y + Y2 = 15 Solving for variable 'Y'. Reorder the terms: -15 + -3Y + Y2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -3Y + Y2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + -3Y + 15 + Y2 = 0 + 15 Reorder the terms: -15 + 15 + -3Y + Y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -3Y + Y2 = 0 + 15 -3Y + Y2 = 0 + 15 Combine like terms: 0 + 15 = 15 -3Y + Y2 = 15 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 = 15 + 2.25 Reorder the terms: 2.25 + -3Y + Y2 = 15 + 2.25 Combine like terms: 15 + 2.25 = 17.25 2.25 + -3Y + Y2 = 17.25 Factor a perfect square on the left side: (Y + -1.5)(Y + -1.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (Y + -1.5) equal to 4.153311931 and -4.153311931.Subproblem 1
Y + -1.5 = 4.153311931 Simplifying Y + -1.5 = 4.153311931 Reorder the terms: -1.5 + Y = 4.153311931 Solving -1.5 + Y = 4.153311931 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 = 4.153311931 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + Y = 4.153311931 + 1.5 Y = 4.153311931 + 1.5 Combine like terms: 4.153311931 + 1.5 = 5.653311931 Y = 5.653311931 Simplifying Y = 5.653311931Subproblem 2
Y + -1.5 = -4.153311931 Simplifying Y + -1.5 = -4.153311931 Reorder the terms: -1.5 + Y = -4.153311931 Solving -1.5 + Y = -4.153311931 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 = -4.153311931 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + Y = -4.153311931 + 1.5 Y = -4.153311931 + 1.5 Combine like terms: -4.153311931 + 1.5 = -2.653311931 Y = -2.653311931 Simplifying Y = -2.653311931Solution
The solution to the problem is based on the solutions from the subproblems. Y = {5.653311931, -2.653311931}
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