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Simplifying x2 + 1.8 * 0.001x + -1.8 * 0.0001 = 0 Multiply 1.8 * 0.001 x2 + 0.0018x + -1.8 * 0.0001 = 0 Multiply -1.8 * 0.0001 x2 + 0.0018x + -0.00018 = 0 Reorder the terms: -0.00018 + 0.0018x + x2 = 0 Solving -0.00018 + 0.0018x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.00018' to each side of the equation. -0.00018 + 0.0018x + 0.00018 + x2 = 0 + 0.00018 Reorder the terms: -0.00018 + 0.00018 + 0.0018x + x2 = 0 + 0.00018 Combine like terms: -0.00018 + 0.00018 = 0.00000 0.00000 + 0.0018x + x2 = 0 + 0.00018 0.0018x + x2 = 0 + 0.00018 Combine like terms: 0 + 0.00018 = 0.00018 0.0018x + x2 = 0.00018 The x term is 0.0018x. Take half its coefficient (0.0009). Square it (0.00000081) and add it to both sides. Add '0.00000081' to each side of the equation. 0.0018x + 0.00000081 + x2 = 0.00018 + 0.00000081 Reorder the terms: 0.00000081 + 0.0018x + x2 = 0.00018 + 0.00000081 Combine like terms: 0.00018 + 0.00000081 = 0.00018081 0.00000081 + 0.0018x + x2 = 0.00018081 Factor a perfect square on the left side: (x + 0.0009)(x + 0.0009) = 0.00018081 Calculate the square root of the right side: 0.013446561 Break this problem into two subproblems by setting (x + 0.0009) equal to 0.013446561 and -0.013446561.Subproblem 1
x + 0.0009 = 0.013446561 Simplifying x + 0.0009 = 0.013446561 Reorder the terms: 0.0009 + x = 0.013446561 Solving 0.0009 + x = 0.013446561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0009' to each side of the equation. 0.0009 + -0.0009 + x = 0.013446561 + -0.0009 Combine like terms: 0.0009 + -0.0009 = 0.0000 0.0000 + x = 0.013446561 + -0.0009 x = 0.013446561 + -0.0009 Combine like terms: 0.013446561 + -0.0009 = 0.012546561 x = 0.012546561 Simplifying x = 0.012546561Subproblem 2
x + 0.0009 = -0.013446561 Simplifying x + 0.0009 = -0.013446561 Reorder the terms: 0.0009 + x = -0.013446561 Solving 0.0009 + x = -0.013446561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0009' to each side of the equation. 0.0009 + -0.0009 + x = -0.013446561 + -0.0009 Combine like terms: 0.0009 + -0.0009 = 0.0000 0.0000 + x = -0.013446561 + -0.0009 x = -0.013446561 + -0.0009 Combine like terms: -0.013446561 + -0.0009 = -0.014346561 x = -0.014346561 Simplifying x = -0.014346561Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.012546561, -0.014346561}
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