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Simplifying 0.00000529 = 0.00000225(x * x) + (0.00000625)(1 + -1x)(1 + -1x) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) Multiply x * x 0.00000529 = 0.00000225(x2) + (0.00000625)(1 + -1x)(1 + -1x) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) Multiply (1 + -1x) * (1 + -1x) 0.00000529 = 0.00000225x2 + 0.00000625(1(1 + -1x) + -1x * (1 + -1x)) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) 0.00000529 = 0.00000225x2 + 0.00000625((1 * 1 + -1x * 1) + -1x * (1 + -1x)) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) 0.00000529 = 0.00000225x2 + 0.00000625((1 + -1x) + -1x * (1 + -1x)) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) 0.00000529 = 0.00000225x2 + 0.00000625(1 + -1x + (1 * -1x + -1x * -1x)) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) 0.00000529 = 0.00000225x2 + 0.00000625(1 + -1x + (-1x + 1x2)) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) Combine like terms: -1x + -1x = -2x 0.00000529 = 0.00000225x2 + 0.00000625(1 + -2x + 1x2) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) 0.00000529 = 0.00000225x2 + (1 * 0.00000625 + -2x * 0.00000625 + 1x2 * 0.00000625) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) 0.00000529 = 0.00000225x2 + (0.00000625 + -0.0000125x + 0.00000625x2) + 2 * 0.6 * 0.0015 * 0.0025x(1 + -1x) Multiply 2 * 0.6 0.00000529 = 0.00000225x2 + 0.00000625 + -0.0000125x + 0.00000625x2 + 1.2 * 0.0015 * 0.0025x(1 + -1x) Multiply 1.2 * 0.0015 0.00000529 = 0.00000225x2 + 0.00000625 + -0.0000125x + 0.00000625x2 + 0.0018 * 0.0025x(1 + -1x) Multiply 0.0018 * 0.0025 0.00000529 = 0.00000225x2 + 0.00000625 + -0.0000125x + 0.00000625x2 + 0.0000045x(1 + -1x) 0.00000529 = 0.00000225x2 + 0.00000625 + -0.0000125x + 0.00000625x2 + (1 * 0.0000045x + -1x * 0.0000045x) 0.00000529 = 0.00000225x2 + 0.00000625 + -0.0000125x + 0.00000625x2 + (0.0000045x + -0.0000045x2) Reorder the terms: 0.00000529 = 0.00000625 + -0.0000125x + 0.0000045x + 0.00000225x2 + 0.00000625x2 + -0.0000045x2 Combine like terms: -0.0000125x + 0.0000045x = -0.000008x 0.00000529 = 0.00000625 + -0.000008x + 0.00000225x2 + 0.00000625x2 + -0.0000045x2 Combine like terms: 0.00000225x2 + 0.00000625x2 = 0.0000085x2 0.00000529 = 0.00000625 + -0.000008x + 0.0000085x2 + -0.0000045x2 Combine like terms: 0.0000085x2 + -0.0000045x2 = 0.000004x2 0.00000529 = 0.00000625 + -0.000008x + 0.000004x2 Solving 0.00000529 = 0.00000625 + -0.000008x + 0.000004x2 Solving for variable 'x'. Combine like terms: 0.00000529 + -0.00000625 = -0.00000096 -0.00000096 + 0.000008x + -0.000004x2 = 0.00000625 + -0.000008x + 0.000004x2 + -0.00000625 + 0.000008x + -0.000004x2 Reorder the terms: -0.00000096 + 0.000008x + -0.000004x2 = 0.00000625 + -0.00000625 + -0.000008x + 0.000008x + 0.000004x2 + -0.000004x2 Combine like terms: 0.00000625 + -0.00000625 = 0.00000000 -0.00000096 + 0.000008x + -0.000004x2 = 0.00000000 + -0.000008x + 0.000008x + 0.000004x2 + -0.000004x2 -0.00000096 + 0.000008x + -0.000004x2 = -0.000008x + 0.000008x + 0.000004x2 + -0.000004x2 Combine like terms: -0.000008x + 0.000008x = 0.000000 -0.00000096 + 0.000008x + -0.000004x2 = 0.000000 + 0.000004x2 + -0.000004x2 -0.00000096 + 0.000008x + -0.000004x2 = 0.000004x2 + -0.000004x2 Combine like terms: 0.000004x2 + -0.000004x2 = 0.000000 -0.00000096 + 0.000008x + -0.000004x2 = 0.000000 Begin completing the square. Divide all terms by -0.000004 the coefficient of the squared term: Divide each side by '-0.000004'. 0.24 + -2x + x2 = 0 Move the constant term to the right: Add '-0.24' to each side of the equation. 0.24 + -2x + -0.24 + x2 = 0 + -0.24 Reorder the terms: 0.24 + -0.24 + -2x + x2 = 0 + -0.24 Combine like terms: 0.24 + -0.24 = 0.00 0.00 + -2x + x2 = 0 + -0.24 -2x + x2 = 0 + -0.24 Combine like terms: 0 + -0.24 = -0.24 -2x + x2 = -0.24 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.24 + 1 Reorder the terms: 1 + -2x + x2 = -0.24 + 1 Combine like terms: -0.24 + 1 = 0.76 1 + -2x + x2 = 0.76 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (x + -1) equal to 0.871779789 and -0.871779789.Subproblem 1
x + -1 = 0.871779789 Simplifying x + -1 = 0.871779789 Reorder the terms: -1 + x = 0.871779789 Solving -1 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.871779789 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.871779789 + 1 x = 0.871779789 + 1 Combine like terms: 0.871779789 + 1 = 1.871779789 x = 1.871779789 Simplifying x = 1.871779789Subproblem 2
x + -1 = -0.871779789 Simplifying x + -1 = -0.871779789 Reorder the terms: -1 + x = -0.871779789 Solving -1 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.871779789 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.871779789 + 1 x = -0.871779789 + 1 Combine like terms: -0.871779789 + 1 = 0.128220211 x = 0.128220211 Simplifying x = 0.128220211Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.871779789, 0.128220211}
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