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Simplifying 12 + -5Y2 = 1Y Solving 12 + -5Y2 = 1Y Solving for variable 'Y'. Reorder the terms: 12 + -1Y + -5Y2 = 1Y + -1Y Combine like terms: 1Y + -1Y = 0 12 + -1Y + -5Y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + 0.2Y + Y2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.2Y + 2.4 + Y2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.2Y + Y2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.2Y + Y2 = 0 + 2.4 0.2Y + Y2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 0.2Y + Y2 = 2.4 The Y term is 0.2Y. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2Y + 0.01 + Y2 = 2.4 + 0.01 Reorder the terms: 0.01 + 0.2Y + Y2 = 2.4 + 0.01 Combine like terms: 2.4 + 0.01 = 2.41 0.01 + 0.2Y + Y2 = 2.41 Factor a perfect square on the left side: (Y + 0.1)(Y + 0.1) = 2.41 Calculate the square root of the right side: 1.55241747 Break this problem into two subproblems by setting (Y + 0.1) equal to 1.55241747 and -1.55241747.Subproblem 1
Y + 0.1 = 1.55241747 Simplifying Y + 0.1 = 1.55241747 Reorder the terms: 0.1 + Y = 1.55241747 Solving 0.1 + Y = 1.55241747 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + Y = 1.55241747 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + Y = 1.55241747 + -0.1 Y = 1.55241747 + -0.1 Combine like terms: 1.55241747 + -0.1 = 1.45241747 Y = 1.45241747 Simplifying Y = 1.45241747Subproblem 2
Y + 0.1 = -1.55241747 Simplifying Y + 0.1 = -1.55241747 Reorder the terms: 0.1 + Y = -1.55241747 Solving 0.1 + Y = -1.55241747 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + Y = -1.55241747 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + Y = -1.55241747 + -0.1 Y = -1.55241747 + -0.1 Combine like terms: -1.55241747 + -0.1 = -1.65241747 Y = -1.65241747 Simplifying Y = -1.65241747Solution
The solution to the problem is based on the solutions from the subproblems. Y = {1.45241747, -1.65241747}
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