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Simplifying 2 + 2Y + -1Y2 = 0 Solving 2 + 2Y + -1Y2 = 0 Solving for variable 'Y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -2Y + Y2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2Y + 2 + Y2 = 0 + 2 Reorder the terms: -2 + 2 + -2Y + Y2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2Y + Y2 = 0 + 2 -2Y + Y2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2Y + Y2 = 2 The Y term is -2Y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2Y + 1 + Y2 = 2 + 1 Reorder the terms: 1 + -2Y + Y2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + -2Y + Y2 = 3 Factor a perfect square on the left side: (Y + -1)(Y + -1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (Y + -1) equal to 1.732050808 and -1.732050808.Subproblem 1
Y + -1 = 1.732050808 Simplifying Y + -1 = 1.732050808 Reorder the terms: -1 + Y = 1.732050808 Solving -1 + Y = 1.732050808 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + Y = 1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + Y = 1.732050808 + 1 Y = 1.732050808 + 1 Combine like terms: 1.732050808 + 1 = 2.732050808 Y = 2.732050808 Simplifying Y = 2.732050808Subproblem 2
Y + -1 = -1.732050808 Simplifying Y + -1 = -1.732050808 Reorder the terms: -1 + Y = -1.732050808 Solving -1 + Y = -1.732050808 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + Y = -1.732050808 + 1 Combine like terms: -1 + 1 = 0 0 + Y = -1.732050808 + 1 Y = -1.732050808 + 1 Combine like terms: -1.732050808 + 1 = -0.732050808 Y = -0.732050808 Simplifying Y = -0.732050808Solution
The solution to the problem is based on the solutions from the subproblems. Y = {2.732050808, -0.732050808}
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