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Simplifying X = X2 + 0.00051X + -0.0000255 Reorder the terms: X = -0.0000255 + 0.00051X + X2 Solving X = -0.0000255 + 0.00051X + X2 Solving for variable 'X'. Reorder the terms: 0.0000255 + X + -0.00051X + -1X2 = -0.0000255 + 0.00051X + X2 + 0.0000255 + -0.00051X + -1X2 Combine like terms: X + -0.00051X = 0.99949X 0.0000255 + 0.99949X + -1X2 = -0.0000255 + 0.00051X + X2 + 0.0000255 + -0.00051X + -1X2 Reorder the terms: 0.0000255 + 0.99949X + -1X2 = -0.0000255 + 0.0000255 + 0.00051X + -0.00051X + X2 + -1X2 Combine like terms: -0.0000255 + 0.0000255 = 0.0000000 0.0000255 + 0.99949X + -1X2 = 0.0000000 + 0.00051X + -0.00051X + X2 + -1X2 0.0000255 + 0.99949X + -1X2 = 0.00051X + -0.00051X + X2 + -1X2 Combine like terms: 0.00051X + -0.00051X = 0.00000 0.0000255 + 0.99949X + -1X2 = 0.00000 + X2 + -1X2 0.0000255 + 0.99949X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 0.0000255 + 0.99949X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.0000255 + -0.99949X + X2 = 0 Move the constant term to the right: Add '0.0000255' to each side of the equation. -0.0000255 + -0.99949X + 0.0000255 + X2 = 0 + 0.0000255 Reorder the terms: -0.0000255 + 0.0000255 + -0.99949X + X2 = 0 + 0.0000255 Combine like terms: -0.0000255 + 0.0000255 = 0.0000000 0.0000000 + -0.99949X + X2 = 0 + 0.0000255 -0.99949X + X2 = 0 + 0.0000255 Combine like terms: 0 + 0.0000255 = 0.0000255 -0.99949X + X2 = 0.0000255 The X term is -0.99949X. Take half its coefficient (-0.499745). Square it (0.2497450650) and add it to both sides. Add '0.2497450650' to each side of the equation. -0.99949X + 0.2497450650 + X2 = 0.0000255 + 0.2497450650 Reorder the terms: 0.2497450650 + -0.99949X + X2 = 0.0000255 + 0.2497450650 Combine like terms: 0.0000255 + 0.2497450650 = 0.249770565 0.2497450650 + -0.99949X + X2 = 0.249770565 Factor a perfect square on the left side: (X + -0.499745)(X + -0.499745) = 0.249770565 Calculate the square root of the right side: 0.499770512 Break this problem into two subproblems by setting (X + -0.499745) equal to 0.499770512 and -0.499770512.Subproblem 1
X + -0.499745 = 0.499770512 Simplifying X + -0.499745 = 0.499770512 Reorder the terms: -0.499745 + X = 0.499770512 Solving -0.499745 + X = 0.499770512 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.499745' to each side of the equation. -0.499745 + 0.499745 + X = 0.499770512 + 0.499745 Combine like terms: -0.499745 + 0.499745 = 0.000000 0.000000 + X = 0.499770512 + 0.499745 X = 0.499770512 + 0.499745 Combine like terms: 0.499770512 + 0.499745 = 0.999515512 X = 0.999515512 Simplifying X = 0.999515512Subproblem 2
X + -0.499745 = -0.499770512 Simplifying X + -0.499745 = -0.499770512 Reorder the terms: -0.499745 + X = -0.499770512 Solving -0.499745 + X = -0.499770512 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.499745' to each side of the equation. -0.499745 + 0.499745 + X = -0.499770512 + 0.499745 Combine like terms: -0.499745 + 0.499745 = 0.000000 0.000000 + X = -0.499770512 + 0.499745 X = -0.499770512 + 0.499745 Combine like terms: -0.499770512 + 0.499745 = -0.000025512 X = -0.000025512 Simplifying X = -0.000025512Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.999515512, -0.000025512}
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