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Simplifying (0.55 + -1X)(1.55 + -1X) = 0.3045 + 0.21X Multiply (0.55 + -1X) * (1.55 + -1X) (0.55(1.55 + -1X) + -1X * (1.55 + -1X)) = 0.3045 + 0.21X ((1.55 * 0.55 + -1X * 0.55) + -1X * (1.55 + -1X)) = 0.3045 + 0.21X ((0.8525 + -0.55X) + -1X * (1.55 + -1X)) = 0.3045 + 0.21X (0.8525 + -0.55X + (1.55 * -1X + -1X * -1X)) = 0.3045 + 0.21X (0.8525 + -0.55X + (-1.55X + 1X2)) = 0.3045 + 0.21X Combine like terms: -0.55X + -1.55X = -2.1X (0.8525 + -2.1X + 1X2) = 0.3045 + 0.21X Solving 0.8525 + -2.1X + 1X2 = 0.3045 + 0.21X Solving for variable 'X'. Reorder the terms: 0.8525 + -0.3045 + -2.1X + -0.21X + 1X2 = 0.3045 + 0.21X + -0.3045 + -0.21X Combine like terms: 0.8525 + -0.3045 = 0.548 0.548 + -2.1X + -0.21X + 1X2 = 0.3045 + 0.21X + -0.3045 + -0.21X Combine like terms: -2.1X + -0.21X = -2.31X 0.548 + -2.31X + 1X2 = 0.3045 + 0.21X + -0.3045 + -0.21X Reorder the terms: 0.548 + -2.31X + 1X2 = 0.3045 + -0.3045 + 0.21X + -0.21X Combine like terms: 0.3045 + -0.3045 = 0.0000 0.548 + -2.31X + 1X2 = 0.0000 + 0.21X + -0.21X 0.548 + -2.31X + 1X2 = 0.21X + -0.21X Combine like terms: 0.21X + -0.21X = 0.00 0.548 + -2.31X + 1X2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-0.548' to each side of the equation. 0.548 + -2.31X + -0.548 + X2 = 0.00 + -0.548 Reorder the terms: 0.548 + -0.548 + -2.31X + X2 = 0.00 + -0.548 Combine like terms: 0.548 + -0.548 = 0.000 0.000 + -2.31X + X2 = 0.00 + -0.548 -2.31X + X2 = 0.00 + -0.548 Combine like terms: 0.00 + -0.548 = -0.548 -2.31X + X2 = -0.548 The X term is -2.31X. Take half its coefficient (-1.155). Square it (1.334025) and add it to both sides. Add '1.334025' to each side of the equation. -2.31X + 1.334025 + X2 = -0.548 + 1.334025 Reorder the terms: 1.334025 + -2.31X + X2 = -0.548 + 1.334025 Combine like terms: -0.548 + 1.334025 = 0.786025 1.334025 + -2.31X + X2 = 0.786025 Factor a perfect square on the left side: (X + -1.155)(X + -1.155) = 0.786025 Calculate the square root of the right side: 0.88658051 Break this problem into two subproblems by setting (X + -1.155) equal to 0.88658051 and -0.88658051.Subproblem 1
X + -1.155 = 0.88658051 Simplifying X + -1.155 = 0.88658051 Reorder the terms: -1.155 + X = 0.88658051 Solving -1.155 + X = 0.88658051 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.155' to each side of the equation. -1.155 + 1.155 + X = 0.88658051 + 1.155 Combine like terms: -1.155 + 1.155 = 0.000 0.000 + X = 0.88658051 + 1.155 X = 0.88658051 + 1.155 Combine like terms: 0.88658051 + 1.155 = 2.04158051 X = 2.04158051 Simplifying X = 2.04158051Subproblem 2
X + -1.155 = -0.88658051 Simplifying X + -1.155 = -0.88658051 Reorder the terms: -1.155 + X = -0.88658051 Solving -1.155 + X = -0.88658051 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.155' to each side of the equation. -1.155 + 1.155 + X = -0.88658051 + 1.155 Combine like terms: -1.155 + 1.155 = 0.000 0.000 + X = -0.88658051 + 1.155 X = -0.88658051 + 1.155 Combine like terms: -0.88658051 + 1.155 = 0.26841949 X = 0.26841949 Simplifying X = 0.26841949Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.04158051, 0.26841949}
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