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Simplifying 0 = -1X2 + -1X + 3.55 Reorder the terms: 0 = 3.55 + -1X + -1X2 Solving 0 = 3.55 + -1X + -1X2 Solving for variable 'X'. Combine like terms: 0 + -3.55 = -3.55 -3.55 + X + X2 = 3.55 + -1X + -1X2 + -3.55 + X + X2 Reorder the terms: -3.55 + X + X2 = 3.55 + -3.55 + -1X + X + -1X2 + X2 Combine like terms: 3.55 + -3.55 = 0.00 -3.55 + X + X2 = 0.00 + -1X + X + -1X2 + X2 -3.55 + X + X2 = -1X + X + -1X2 + X2 Combine like terms: -1X + X = 0 -3.55 + X + X2 = 0 + -1X2 + X2 -3.55 + X + X2 = -1X2 + X2 Combine like terms: -1X2 + X2 = 0 -3.55 + X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '3.55' to each side of the equation. -3.55 + X + 3.55 + X2 = 0 + 3.55 Reorder the terms: -3.55 + 3.55 + X + X2 = 0 + 3.55 Combine like terms: -3.55 + 3.55 = 0.00 0.00 + X + X2 = 0 + 3.55 X + X2 = 0 + 3.55 Combine like terms: 0 + 3.55 = 3.55 X + X2 = 3.55 The X term is X. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. X + 0.25 + X2 = 3.55 + 0.25 Reorder the terms: 0.25 + X + X2 = 3.55 + 0.25 Combine like terms: 3.55 + 0.25 = 3.8 0.25 + X + X2 = 3.8 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 3.8 Calculate the square root of the right side: 1.949358869 Break this problem into two subproblems by setting (X + 0.5) equal to 1.949358869 and -1.949358869.Subproblem 1
X + 0.5 = 1.949358869 Simplifying X + 0.5 = 1.949358869 Reorder the terms: 0.5 + X = 1.949358869 Solving 0.5 + X = 1.949358869 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 1.949358869 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 1.949358869 + -0.5 X = 1.949358869 + -0.5 Combine like terms: 1.949358869 + -0.5 = 1.449358869 X = 1.449358869 Simplifying X = 1.449358869Subproblem 2
X + 0.5 = -1.949358869 Simplifying X + 0.5 = -1.949358869 Reorder the terms: 0.5 + X = -1.949358869 Solving 0.5 + X = -1.949358869 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -1.949358869 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -1.949358869 + -0.5 X = -1.949358869 + -0.5 Combine like terms: -1.949358869 + -0.5 = -2.449358869 X = -2.449358869 Simplifying X = -2.449358869Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.449358869, -2.449358869}
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