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Simplifying ((0.79 + -1X)(0.21 + -1X)) = 0.0011 Multiply (0.79 + -1X) * (0.21 + -1X) ((0.79(0.21 + -1X) + -1X * (0.21 + -1X))) = 0.0011 (((0.21 * 0.79 + -1X * 0.79) + -1X * (0.21 + -1X))) = 0.0011 (((0.1659 + -0.79X) + -1X * (0.21 + -1X))) = 0.0011 ((0.1659 + -0.79X + (0.21 * -1X + -1X * -1X))) = 0.0011 ((0.1659 + -0.79X + (-0.21X + 1X2))) = 0.0011 Combine like terms: -0.79X + -0.21X = -1X ((0.1659 + -1X + 1X2)) = 0.0011 (0.1659 + -1X + 1X2) = 0.0011 Remove parenthesis around (0.1659 + -1X + 1X2) 0.1659 + -1X + 1X2 = 0.0011 Solving 0.1659 + -1X + 1X2 = 0.0011 Solving for variable 'X'. Reorder the terms: 0.1659 + -0.0011 + -1X + 1X2 = 0.0011 + -0.0011 Combine like terms: 0.1659 + -0.0011 = 0.1648 0.1648 + -1X + 1X2 = 0.0011 + -0.0011 Combine like terms: 0.0011 + -0.0011 = 0.0000 0.1648 + -1X + 1X2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '-0.1648' to each side of the equation. 0.1648 + -1X + -0.1648 + X2 = 0.0000 + -0.1648 Reorder the terms: 0.1648 + -0.1648 + -1X + X2 = 0.0000 + -0.1648 Combine like terms: 0.1648 + -0.1648 = 0.0000 0.0000 + -1X + X2 = 0.0000 + -0.1648 -1X + X2 = 0.0000 + -0.1648 Combine like terms: 0.0000 + -0.1648 = -0.1648 -1X + X2 = -0.1648 The X term is -1X. 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. -1X + 0.25 + X2 = -0.1648 + 0.25 Reorder the terms: 0.25 + -1X + X2 = -0.1648 + 0.25 Combine like terms: -0.1648 + 0.25 = 0.0852 0.25 + -1X + X2 = 0.0852 Factor a perfect square on the left side: (X + -0.5)(X + -0.5) = 0.0852 Calculate the square root of the right side: 0.29189039 Break this problem into two subproblems by setting (X + -0.5) equal to 0.29189039 and -0.29189039.Subproblem 1
X + -0.5 = 0.29189039 Simplifying X + -0.5 = 0.29189039 Reorder the terms: -0.5 + X = 0.29189039 Solving -0.5 + X = 0.29189039 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 = 0.29189039 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = 0.29189039 + 0.5 X = 0.29189039 + 0.5 Combine like terms: 0.29189039 + 0.5 = 0.79189039 X = 0.79189039 Simplifying X = 0.79189039Subproblem 2
X + -0.5 = -0.29189039 Simplifying X + -0.5 = -0.29189039 Reorder the terms: -0.5 + X = -0.29189039 Solving -0.5 + X = -0.29189039 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 = -0.29189039 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + X = -0.29189039 + 0.5 X = -0.29189039 + 0.5 Combine like terms: -0.29189039 + 0.5 = 0.20810961 X = 0.20810961 Simplifying X = 0.20810961Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.79189039, 0.20810961}
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